First, you will need a tarte Tatin tin or a metal-handled frying pan measuring 24cm in diameter.

Then, put the flour into the bowl of a food processor, add 120g butter in small pieces and process to the texture of fine breadcrumbs. Add the egg yolk, thyme leaves and 3 tablespoons of the grated Parmesan, process briefly, then transfer to a lightly floured board and bring together into a ball. Of course, you can do this by hand if you wish, rubbing the flour and butter together with your thumb and fingertips (a peaceful flour-dusted thing to do), then fold in the yolk, thyme and cheese. Wrap in baking parchment or place in a bowl and cover, and leave to rest in the fridge.

Set the oven at 200°C/Gas 6. Peel the shallots, then halve lengthways. Melt the remaining 30g of butter with the oil in the tin or frying pan over a moderate heat, then add the shallots, cut side down. Let them brown lightly, then turn to let the other side colour. Meanwhile, halve, core and slice each apple into eight segments. Remove the shallots from the pan, then add the apples, letting them soften and turn lightly gold. Scatter over the remaining tablespoon of grated Parmesan, then return the shallots.

Roll the pastry out to a good 3cm larger than the tin or frying pan. Lay the pastry over the shallots and apples, tucking in the overhanging dough. Bake for twenty-five minutes, until the pastry is pale biscuit-coloured and the butter is bubbling round the edges. Remove from the oven, leave to settle for ten minutes, then turn out onto a serving plate.

From Greenfeast: Autumn, Winter, by Nigel Slater, published by 4th Estate Books. Photographs: Jonathan Lovekin