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To make the pastry, put the flour, 50g hazelnuts and ½ tsp salt into a food processor. Give it a quick pulse to disperse the nuts through the flour, then add the butter and blitz until the mixture resembles rough breadcrumbs. Add the egg and 3 tbsp ice-cold water, and blitz again until the pastry is just coming together – if the pastry feels dry, add a tbsp more water and pulse again. Flatten into a disc, wrap in cling film and chill in the fridge for 30 mins until firm.
Heat oven to 200C/180C fan/gas 6. Melt the butter in a frying pan. Once foaming, add the sage leaves and fry for a min or so until crisp. Transfer to a plate with a slotted spoon and set aside. Mix the oil with the butter in the pan. Put the squash chunks in a roasting tin, sprinkle over the chilli flakes and some seasoning, then pour over the butter mixture. Toss together so that all the pieces of squash are coated, then roast for 35 mins until tender but holding their shape. Set aside to cool.
Roll the pastry into a circle roughly 3mm thick on a floured surface, then use it to line a deep 25cm tart tin. Prick the base all over with a fork, then return to the fridge for 20 mins to firm up, or chill it in the freezer for a few minutes.
Meanwhile, chop three-quarters of the sage leaves. Whisk the cream with the milk and eggs in a bowl until combined, add a good grating of nutmeg, season well, then stir through the feta, cooled squash and chopped sage.
Line the pastry with baking parchment, fill with baking beans or dried rice and bake for 15 mins until the sides of the pastry are holding their shape. Remove the paper and beans and bake for 10 mins more until the pastry is lightly golden. Reduce the oven to 160C/140C fan/gas 3.
Pour the quiche filling into the pastry case, then scatter over the rest of the hazelnuts and sage leaves. Return to the oven for 40-50 mins or until the filling is just set. Cool to room temperature before serving.