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Heat oven to 200C/180C fan/gas 6. Toss the squash in a roasting tin with the garlic, rosemary and thyme leaves. Drizzle with 2 tbsp oil and season well. Roast for 40 mins or until soft and starting to brown. Remove and squeeze the garlic out of its skin, mash and gently mix with the squash, than set aside to cool.
Heat remaining oil in a small pan and fry the onion until soft and lightly golden. Add the mushroom and fry for 3-4 mins more. Remove from heat and set aside. In a large bowl, mix the chestnuts, herbs, cheese, and nutmeg. Stir in mushrooms and squash mixture, taking care not to break up the squash too much. Season well.
Roll a third of the pastry into a rectangle measuring 12 x 30cm. Place on a baking tray and pierce all over with a fork, brush with beaten egg and bake for 10 mins until lightly golden and slightly risen.
Roll out the remaining two-thirds to a rectangle slightly larger than the base then, using a sharp knife, slash diagonally. Pile the filling onto the partly-cooked base leaving a 1cm border. Brush the border with a little beaten egg and carefully lay the uncooked pastry on top, pressing down the edges to seal. Glaze top with a little more egg and bake for 30-35 mins until the pastry is golden, risen and cooked through.