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To make the pastry, put the flour, butter and sugar in the bowl of food processor and pulse until it looks like breadcrumbs. Add the egg yolk and 1 tbsp cold water, then pulse again until it forms a ball. Wrap and chill for 30 mins.
For the frangipane, beat the butter and sugar together until pale and fluffy, add the egg, whisk again, then fold in the ground almonds to make a paste. Cut the peaches into thin slices, then toss in a bowl with the lemon juice, cornflour, vanilla and icing sugar. Mix gently until the fruit is coated and the cornflour dissolved. Heat the oven to 200C/180C fan/gas 6 and heat a large baking sheet on the middle shelf.
Roll the pastry out in between two pieces of baking parchment to a large disc about 5mm thick and 35cm in diameter. Remove the top layer of parchment, draw a 30cm circle onto it, cut it out, and use as a template to cut out a disc of pastry, or roughly trim the pastry into a circle by eye for a more rustic look.
Smooth the frangipane over the middle of the pastry with a spatula, leaving a 5cm border around the edge. Arrange the peach slices over the top in a pattern, either in a circle or little fans of fruit.
Fold in the edges of the pastry to slightly overlap the fruit. Brush with the beaten egg and sprinkle over the demerara, then transfer to the hot baking sheet using the parchment.
Bake for 30-35 mins until the pastry is golden and the fruit looks soft. Leave to cool to room temperature. Heat the jam in the microwave for a few seconds, or in a small pan until warm and runny, then use to glaze the fruit. Serve with thick cream or ice cream.
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