The first things that strike you are the olive trees. On the way from Bari airport to our first hill town, Ostuni, we pass untold hectares of them. When we visit the Masseria Brancati, we get to see them close up, laden with leaves and fruit, which is still unripe – it’s August and the earliest harvest is still a couple of months away. Some of the trees, named the monumentali, are very, very old – 2,500 years or more: their trunks are several feet wide, gnarled, looking generally grumpy at what they’ve seen.

Puglia produces 40% of Italy’s olive oil. But this ancient part of the nation’s culture is vulnerable, as evidenced when you drive past Brindisi and see the road – the old Appian Way from Rome – lined by thousand upon thousand of dead trees, standing upright but with their leaves scorched. They’re the victims of a single subspecies of bacterium, the xylella fastidiosa subs. pauca: since 2013, farmers and government scientists have been engaged in a desperate struggle to save the olive trees: there are signs of some recovering or being replanted, but the lines of brown trees are still a desperately sad sight.

In Italy, food defines everything. And Puglia is where the food is grown, so it’s all about doing simple things with the local ingredients. The centro storico of Ostuni is packed with shops selling local food items to the well-heeled tourists from further north, of which the most important is olive oil. Apart from details of terroir and whether or not the oil is organic, the principal differences between oils lie in whether or not they are first pressing (the Italians tell you to keep extra virgin olive oil for salads and not use it for cooking) and the harvest date: early harvest olives (mid-October) give an oil with a distinctive strong flavour, whereas late harvest olives can give a smooth oil with a long aftertaste.

Almonds are another important crop. If you’re an ice-cream lover, don’t miss their combined fichi e mandorle (fig and almond) flavour, and the shops have plenty of almond biscuits of various types. There are many types of hard biscuits (including the biscotti type familiar to us outside Italy), but my downfall was the mouth-watering soft ones, something between an almond biscuit and marzipan, that we bought from the Furne di Porta Nova bakery, towards the east of the old city in Ostuni. The bakery also makes focaccia, the Puglian version being delightfully light, with far less oil and salt than I’ve had elsewhere, and usually laden with olives and cherry tomatoes. Apart from focaccia, my favourite bread here is their equivalent of the Spanish pan rustico, an unevenly shaped sourdough loaf with a hard crust and a delectable soft, moist middle: in at least one bakery we visited, the sourdough starter was made with fruit. Hard crackers (taralli and friselli) are ubiquitous, handed out as snacks with virtually any drink you buy at a bar.

Puglia’s hallmark cheese is burrata: soft, white balls, usually 6 centimetres or so in diameter which are popular both as breakfast and lunch items. Cut into the skin-like outside and a creamy filling gushes forth, delicious on its own or as part of a salad (but be sure to eat fresh burrata the day they’re made – they don’t improve). Lunch plates are also likely to include caciocavallo, a hard cheese made of sheep’s or cow’s milk or, most deliciously, both. There’s also capocollo (a cut of cured pork from the neck and shoulder, somewhat fattier and somewhat stronger tasting than typical prosciutto).

And then, of course, there’s the wine. Various connoisseurs I know are rather dismissive of Puglian wines as being easy drinking and lacking in distinction. Personally, I love Puglian red wines: they’re scented, full of flavour and low on hard tannins. The predominant grapes here are Primitivo (the same variety as the US Zinfandel), Negroamaro and Malvasia nera; there’s a wine called Salice Salentino that blends either two or all three of these. There are others to be discovered: we didn’t get round to Nero di Troia, but the contents of our bottle of Susumaniello vanished without trace in a chorus of yums. I’m less keen on the whites here, but they make a mean summer rosé with Negroamaro.

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A short trip to Matera in the neighbouring province, Basilicata, revealed another truly lovely red wine, Aglianico, said to be one of the oldest wines from Greek times (the name may or may not be a corruption of “Hellenico”). It tells you something about Italian regionalism that Aglianico was nowhere to be seen on the shelves in Puglia, even if you’re only half an hour’s drive from the border. If you’re buying a present for a friendly baker, a neat souvenir from Matera is a wooden bread stamp, used in bygone days to stamp you initials on your loaf when baking it in a communal bread oven.

Even within the province, there is variability according to region. We stayed at Gallipoli on the Salento peninsula (not to be confused with the battle site in faraway Turkey), a town which has been a fishing centre for centuries and is celebrated for its seafood. At the fish market, stalls proudly announce that the produce is “recently fished”: the fish was very good; the clams and mussels were outstanding. The surprise of our trip were the gamberi viole (purple prawns), said to only be available in the Salento area and up there with the most intense-tasting shellfish I’ve ever eaten. When I asked the man in the market how best to cook them, his response was “anchè crudo” (don’t bother and eat them raw). I wimped out and showed them the pan for a couple of minutes and I’m glad I didn’t do more: they were fabulous, but we discovered in one restaurant that they lose their flavour if overcooked by even a minute or so (the restaurant, to be fair, replaced them without demur).

Our experience of Puglian restaurants was that they’re not particularly good at trying to be fancy. But when it comes to taking great fresh ingredients – even humble ones – and cooking them simply, they’re masterful. Portions, by the way, are giant: if you’re trying to leave room for dessert, be wary. Il Pettolino in Gallipoli, Nausikaa in Martina Franca, Il Guercio di Puglia in Alberobello and PerBacco in Locorotondo all served us meals that were thoroughly memorable without a sniff of haute cuisine. We’ll be back.