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Heat oven to 200C/180C fan/gas 6. Peel the onions and cut each into 6 wedges through the root. Heat the oil in a large pan, add onions, then gently fry for 20 mins until softened and lightly coloured.
Add the mushrooms, sugar, salt and pepper and give it a good stir. Gently cook, stirring now and then for a further 5 mins. Stir in the walnuts. Line the base of a 20-23cm sandwich cake tin (not loose-based) with baking parchment. Spoon over the onion mixture and press it down lightly. Crumble the cheese over.
Roll out the pastry and trim to a round, about 5cm larger than the tin. Put the pastry over the filling and tuck in the ends. Bake for 35-40 mins until the pastry is crisp and golden. Cool for 5 mins in the tin, then turn out onto a flat plate and cut into wedges. Serve with a green salad.