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Melt the butter, return to room temperature by adding the water. It must be liquid without butter flakes. Pour over sifted flour and salt and mix on the hook of the mixer, adding the white vinegar at the end. Be careful not to give body to the dough. Make a ball and then cut a cross with a knife to allow the dough to relax better overnight. The next day, roll out the dough crosswise and add the butter shaped into a 2 cm-thick slab. Give 2 single turns then 2 more single turns after 6 hours. At this stage, the puff pastry can either be stored in the freezer or kept in the fridge to give the last two single turns the next day.
Roll out the puff pastry 2mm thick on a lightly floured work surface and shape the edges by hand by bringing the edges of the tart back on themselves to form an edge. Leave to rest overnight.
Heat the milk, vanilla and the first lot of sugar. Froth the yolks and the second lot of sugar and add the cornflour. Mix little by little and bring to a boil for 1 minute. Add the butter in cubes off the heat, empty onto a baking sheet, cover with clingfilm and cool immediately.
Mix all the ingredients in succession except the rum. Emulsify with the flat beater and add the rum then the previously smoothed pastry cream.
Clean the basil leaves under fresh water and dry them gently on absorbent paper. Mix together and store in the freezer to keep the nice green colour. Use as required.
Cover the tart base with cling film or soft baking paper and cover with cherry or mirabelle plum stones. Bake at 180° until the edges are lightly coloured, remove the stones and continue baking until the inside of the tart is coloured, apply a coil of frangipane almond cream, sprinkle with mixed biscuit and arrange the white peach quarters seasoned with basil sugar. Continue baking for as long as it takes to cook the fruit.
Cool on a wire rack to keep all the crispness of the pastry and keep at room temperature until serving.
Corsican Muscat, Sweet Gaillac, Ben Rye de Donnafugata (Sicily)
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