The grandfather is surely far too old to be working. He's gnarled, bent double and leaning against a stack of bricks lest he collapses into the dusty red earth beneath him. I stand a couple of steps away, scrutinising his contorted, calloused limbs and wondering how much of southern Italy's past is written into them; how any living thing could see so much and look this ordinary.

Masseria Branctati's 30 hectares of land – just outside the gleaming white city of Ostuni in the region of Puglia – has about 1,000 centuries-old olive trees, but the one they call the grandfather is the oldest. Not that you'd know it. There's no fencing separating it from the rest; no sign hanging off one of its spindly branches saying '3,000-year-old tree'; in a field of exceptionally old trees, all spaced about 18 metres apart in orderly rows, this just happens to be the most ancient, planted by the local Messapian tribe before either the Greeks or Romans arrived in Puglia.

Incredibly, the grandfather still contributes fruit to Masseria Brancati's olive oil output, yielding about 50kg of olives every two years. (It's measured over two years rather than one, my guide tells me, because yield tends to alternate between low and high from one year to the next.) Just a few steps from where I'm sitting is another, bigger tree with a rotund, hollowed-out trunk that was planted around 2,000 years ago – as the Roman Empire emerged from the wreckage of the Roman Republic – and still produces a two-year yield of 140kg.

That either of these trees is still standing is testament to a reverence for olives and their output that's endured for more than 3,000 years in this narrow strip of land in the 'heel' of Italy – and the first drop of Brancati's extra virgin olive oil I taste explains why. Sitting in a chair on the lawn outside the farmhouse, I mop up the golden liquid with a piece of bread and my brain struggles to keep pace with the layers of flavour and sensation; it's bitter and grassy, with green-apple freshness and a fast-fading aromatic tingle that makes my jaw clench reflexively.

It's hard to overstate the importance of olive oil to Puglia and in particular here, in the Valle d'Itria – a limestone depression that runs, north to south, from Putignano to Ostuni, where great swathes of silvery-green foliage and characteristic red clay soil dominate the landscape wherever you go. No other region produces as much olive oil as Puglia, and it, along with tomatoes and wheat, is the mainstay of an economy that's long been dominated by agriculture.

I mop up the golden liquid with a piece of bread and my brain struggles to keep pace with the layers of flavour

But more than that – and the reason I'm here in the first place – it's the backbone of a cuisine that's astonishingly rich, incredibly varied and intensely regionalised, which probably shouldn't be a surprise in a place where dialects can vary wildly from town to town. While that makes it almost impossible to pin down a definitive style of Pugliese cooking, if the region's cuisines share one common identifier it's a kind of supreme authenticity; food created from spectacularly good produce that, in the right hands, delivers flavours that are both deeply complex and straightforwardly comforting. No matter where you go and what you eat – from meaty little bombette rolls barbecued on the street in Cisternino, to crudo seafood eaten metres from the sea it was hauled from – this is soul food from Italy's deep south.

What Pugliese food isn't – at least according to Puglia-born chef Domingo Schingaro – is the one thing it's frequently described as: cucina povera (poor cooking). The region is, and has long been, one of the poorest in Italy, with a GDP per capita well below the national average and unemployment well above it, but Schingaro, the man behind Michelin-starred Due Camini, doesn't view the cucina povera designation is a particularly useful one.

"I don't think it's cucina povera," he says of Pugliese cooking. "It's the true cuisine, it's the essence of every culinary experience, and you won't find it anywhere else. I have a different vision – there aren't 'poor' or 'rich' dishes, only 'good' or 'bad' dishes. The good ones are those capable of transmitting something special, telling a story and offering surprising flavours."

That's exactly what he's trying to create at Due Camini, the flagship restaurant at Borgo Egnazia, an effortlessly sophisticated luxury hotel near the small port town of Savelletri, about 25km north west of Ostuni. At Due Camini, Puglia's ingredients and dishes are reinterpreted and reframed through a fine-dining lens, though the starting point for most dishes, Schingaro tells me, is his childhood up the coast in Bari. "When I think about a new dish, I like playing with my memories," he explains. "I start from the past, the traditions and the old recipes, and then I try to create something new and surprising to enhance the taste of the genuine Puglian products."

In Pugliese cooking there aren't 'poor' or 'rich' dishes, only 'good' or 'bad' dishes

When I visit, the menu is full of local produce, from meat and seafood – no surprise given Schingaro's father is a fisherman who "taught me everything about the sea, making me discover a world of unexpected tastes" – to rape (turnip tops, often served with Puglia's iconic, ear-shaped orecchiette pasta), femminiello lemons from nearby Gargano, and Torre Canne regina tomatoes.

A speciality of the coast around Borgo Egnazia, pomodoro regina are grown in ocean-facing, cliff-top fields and are usually unirrigated, so they soak up brackish water from the soil. The unusual growing conditions don't just impart a unique flavour – the tomatoes are sweet, tangy and delicious – but cause the tomatoes to develop a thick skin that means, in the right conditions, they can be strung up in bunches called ramasole (traditionally tied up with cotton grown between the rows of tomato plants) and stored for several months. At Due Camini, a single, bright-red regina appears on a plate that also features sea urchin and raw beef from Gargano's native-breed podolica cattle – and the small but potent tomato is the star.

Seafood crudo

Seafood crudo eaten metres from the very sea it was hauled from is the soul food of Italy's deep south

The regina tomato and podolica beef are among 20 products in Puglia (and 312 in the whole of Italy) protected by the Slow Food Presidia project, which is designed to promote and protect traditional products that are in danger of extinction. That's particularly the case when there are cheaper, faster-growing alternatives (as is the case with the regina and podolica), though as Schingaro points out the Puglian people have an unusually strong devotion to agriculture. "I think we still have a deep bond with our land, and there are still many people working fields with love and passion."

I've already seen evidence of this myself, on a bike ride on the gravel paths that cut through the farmland around Borgo Egnazia. My guide, Ketty, takes me through field after field of produce – each more pastoral-perfect than the next – spilling over with everything from tomatoes and wheat to green beans and courgettes. Our destination, though, is a dairy farm called Masseria Lamapecora that specialises in cheese, and in particular mozzarella and its glam relation, burrata.

The farm's pastures, olive groves and barns radiate out from a typically ancient and utilitarian-looking white building, which also happens to contain a small farm shop next to a small room where mozzarella is made. The room is predictably spartan, with beige tiles on the walls and floors and a huge metal sink where the cheesemaker, Omer, is readying his raw materials. In the sink are several plastic buckets and jugs, some empty and others filled with milk and cream from the farm's four breeds of cows, each of which produces milk of a slightly different character. Watching Omer make mozzarella is hypnotic.

I'll spare you the instruction manual, but suffice to say there's a lot of squeezing, wringing and shaping, and plenty of 'shuffling' and stretching on a long wooden paddle that Omer handles with the smooth power and focus of an Olympic kayaker. To make burrata he presses warm mozzarella into the sides of a mould to make a well, into which he pours stracciatella – ragged strips he'd earlier torn off the proto-mozzarella and cooled for a few minutes – mixed with cream. He then closes the top and drops it into cold water to maintain that all-important transition from soft, gently giving mozzarella shell to the cream-drenched innards.

Minutes later I'm sitting a few metres away at a small table heaving with different cheeses – from impossibly light and fresh primo sale (lightly seasoned rounds of curd cheese made that morning by Omer) to pecorino made with strongly flavoured, fattier milk from the farm's sheep; the flavour is extraordinary, with the cognac-like notes of dried fruit and a salty, farmy edge. There's ricotta, too, and mozzarella of course – including Puglia's signature little tied-off knots, called nodini – and right in the middle of it all is a burrata, which I prod and poke with a small plastic spoon, before teasing out the stracciatella and dousing it in extra virgin olive oil from the farm.

I hoover up as much cheese as I can before heaping the rest into a plastic tub for later, and Ketty and I wander out to admire the cows (all of whom have names, by the way); some laze around in the shade of a barn, others have ambled out to the olive grove to nibble grass in the morning sun. While we stand there, idly watching them, cars come in and out to pick up their cheese – few locals go to the market, Ketty tells me, they just go from farm to farm to buy the freshest, best produce from people they know and trust.

Things have changed, though, as the farm's owner tells us when he strides over for a chat; farming's hard work and tiring, and young people don't want to do it anymore. "Sixty years ago there would have been many farms like this, but they've all gone," he says, sparking up a Camel and looking admiringly at his cattle. It's easy to see why protecting artisan production from industrialised alternatives and convenience shopping is such a priority.

Where to stay

Borgo Egnazia

Built to resemble a tumbledown Italian 'borgo', or village, this resort is just about the most effortlessly luxurious place you could imagine. The real star, though, is the food, from experimental fine dining at Due Camini to epically good seafood on the seafront at Cala Masciola. You can book foodie trips, too, to experience the region's cuisine at its most authentic.

From €249 per night B&B, based on two sharing. To book, call +39 080 225 5850 or visit borgoegnazia.com

Masseria Le Carrube

Though it's sister to Borgo Egnazia, Le Carrube is a different proposition altogether. The ancient farmhouse is spartan but sophisticated, with a subtly atmospheric backdrop of olive trees, terracotta soil and rolling hills. Le Carrube's also notable for its vegetarian food, which draws almost exclusively from the surrounding fields and farms.

From €140 per night B&B, based on two sharing. To book, call +39 083 134 2595 or visit masserialecarrubeostuni.it

Back at the hotel a couple of hours later, I'm booked in for lunch at the golf course over the road, San Domenico Golf, which – given the amount of cheese I've just eaten and my total lack of interest in the sport – I'm ashamed to say I'm kind of ambivalent about. I sit down on a table outside, with my wife and one-year-old son, and then the plates begin to arrive from the massaia Mimina – heaps of green beans and tomatoes dressed with little but olive oil; fresh pasta with even fresher pesto; a plate of familiar-looking nodini and local cured meats; more pasta with a pomodoro sauce, which my son polishes off in seconds, prompting the arrival of more plates (all for him).

About two courses past the point where I'd told myself I couldn't possibly eat any more, a casserole dish arrives, and as I open it I get a nose full of richly scented, vaguely oceanic vapour. I peer in and see octopus – stewed, I'm told, in a terracotta pot called a pignata, along with white wine, onion, tomatoes and herbs. Seasoning (and olive oil) aside, that's it. The octopus is tender and the broth is deep and aromatic.

I gaze out at the pea-green fairway, where a couple of golfers stand over a ball doing whatever it is golfers do. I'm sure it's lovely, but they can't possibly be having as good a time as us. This – eating the carefully produced and sensitively cooked fruits of the region, bathed in the sun that imbues it with such flavour and character – is what this area was surely built for, and what locals and visitors have been enjoying for thousands of years. I dig my fork into the pot, skewer a tentacle and continue to honor Puglia with my stomach and my heart.