The kernel of a walnut, if you catch it in the right light, resembles a brain. It's something about the crenellation and the way it fits together in two halves. For this reason, there were ancient Greeks and Romans who believed, in a literal-minded fashion, that walnuts must cure headaches.

Walnuts also act like a brain in a culinary sense. When you cook with walnuts, they affect the whole personality of a dish. They become the controlling mechanism deciding what the predominant taste will be. When you add olive oil to a salad dressing, it's just dressing. But when you add walnut oil, even if olive oil is also present, it becomes walnut oil dressing. Here is my theory of walnuts. They are wonderful when eaten alone, or as the main ingredient in a recipe, but are actually slightly unpleasant when their function is peripheral. Because they will dominate anyway, you may as well let them take control from the offset.

For example, I have never understood why it is conventional to add a handful of walnuts to cakes such as banana bread or carrot cake. To my taste (though I am sure many would disagree), walnuts in this context are unwelcome intruders, whose crunchy texture has deteriorated in the baking, becoming waxy nuggets, sticking in the teeth and spoiling the flavours of the cake with their slight bitterness, especially if they are in any way rancid (which nuts so often are, on account of their high fat content). On the other hand, a cake made from ground walnuts, or a mixture of ground and whole walnuts, is lovely. By the same token, a Waldorf salad is usually horrible, whereas a handful of walnuts eaten with an apple and celery on the side is fine.

Walnuts must never be allowed to become bits. This is one of the reasons why ground walnuts are so good, whether in sweets or in French walnut soup or the salsa di noci used to dress pasta in Liguria, that fantastically rich, garlicky paste, so over the top you have to recline after eating it.

There are 15 separate species of walnuts, but only one is commonly used in this country, the Juglans regia, also known as the Persian walnut, the English walnut or the Italian walnut, depending on where you come from (in Old English, it was known as the nux gallia, or "Gaulish nut"). When the walnut fruit is young and green, in early summer, the whole thing can be eaten, outside and all, though it tastes very sour (this is the kind of walnut often used in pickled walnuts). At a slightly later stage, when the nut is half ripe, the walnut can be preserved in syrup (a Middle Eastern sweetmeat) or candied (a Torinese custom, described by Elizabeth David in Italian Food). But for autumnal cakes and biscuits, the fully ripe brown shelled walnut is best. Here are two examples, one a tart from France and the other a kind of squidgy macaroon, good with coffee.

Gateau aux noix

This is Peter Graham's recipe, taken from Mourjou: the life and food of an Auvergne village, a charming book. The gateau is a little bit like a more subtle, less cloying version of pecan pie.

320g short pastry; 3 eggs, separated; 60g caster sugar;

3 tbsp honey; 110g shelled, finely chopped walnuts; salt

Preheat oven to 180oC. Roll out the pastry and use it to line a 20cm flan tin. Whisk the egg yolks with the sugar and honey until pale, then add the walnuts and mix. Whisk the egg whites with the salt, then fold gently into the walnut mixture. Pour into the lined flan tin and bake for 45 minutes, covering the top with foil towards the end if it looks like burning. Eat warm; enough for four.

Walnut macaroons Makes 15-20

200g walnuts; 120g icing sugar;

2 large egg whites; a pinch of salt;

a dribble of vanilla essence (use Tahitian if you want them to taste French, otherwise Madagascan)

Preheat oven to 170oC. Grind the walnuts and icing sugar together in a food processor until finely pulverised. Whip the whites with the salt until stiff. Combine the two mixtures along with the vanilla (there's too much of the dry ingredients to fold them). Put in spoonfuls, of whatever size you prefer, on lined baking trays. Bake for 10-20 minutes, or until very light brown. Leave to cool on a rack. They should seem underdone when they come out of the oven, because then they will still be soft when you eat them. Another rule of walnuts is that they must never be allowed to burn, even slightly.