First, make the pastry. Tip the flour into a bowl, then add the butter and 1 tsp salt. Rub the butter into the flour using your fingertips until it has a damp, sandy texture. Mix in the thyme leaves. Whisk the egg yolk with 2 tbsp cold water, then use a cutlery knife to mix this into the crumbs until the mixture starts to clump together. Tip the pastry onto a work surface and knead briefly to bring together into a smooth dough, adding up to 1 tbsp more water if the pastry feels too dry. Shape into a disc, wrap in baking parchment and chill for 30 mins, or up to a day.
Heat 2 tbsp of the oil in a large frying pan over a low-medium heat and cook the onions for 20-25 mins until softened and caramelised. Stir in the red wine vinegar and sugar, and cook for 1-2 mins more until the vinegar has bubbled away. Leave to cool slightly.
Cut the squash into 1cm cubes, then tip into a roasting tin and toss with the remaining 1 tbsp oil and some seasoning. Heat the oven to 180C/160C fan/gas 4.
Unwrap the pastry and lightly dust the parchment with flour. Roll the pastry out on the parchment until it’s about ½cm thick and large enough to line the base and side of a 26cm fluted tart tin. (If the edges start to crack as you roll, squeeze them back together.) Keep turning the pastry as you roll it out to make sure it’s an even thickness and doesn’t stick to the parchment.
Line the tin with the pastry, pressing it into the base and up the side, patching any holes with excess pastry. Trim any overhanging pastry so it comes about 1cm above the rim. Reserve any offcuts, as you may need them for patching later. Line the pastry case with the sheet of baking parchment and fill with baking beans or uncooked rice. Bake on the middle shelf of the oven, with the squash on the shelf underneath, for 20 mins.
Remove the pastry case from the oven and lift out the parchment and baking beans. If there are any holes in the pastry, patch these using the reserved pastry offcuts, then lightly beat the egg white and brush this all over the inside of the pastry case. Bake for 5 mins more until biscuity and golden.
When the pastry case is ready, use a small, serrated knife to carefully trim the overhanging pastry. Mix the roasted squash into the caramelised onions along with the thyme leaves.
Whisk the mustard, eggs, cream, half the cheese and some seasoning together in a jug. Spoon the onion and squash mix into the pastry case – it will be quite full. Pour over the egg and cream mixture, then scatter over the remaining cheese.
Reduce the oven to 160C/140C fan/gas 3 and bake the tart on the middle shelf of the oven for 35 mins until golden brown and set. Leave to cool in the tin for at least 30 mins before serving warm, or cool completely and serve cold. Will keep chilled for up to two days.
