Quickly combine the flour, chopped butter, salt and 1–2 tablespoons water to make a shortcrust pastry. Form into a ball, wrap in plastic wrap and put into the refrigerator for about 1 hour.
Then roll out on a floured work surface and use to line a greased tart pan. Cut off the excess by rolling over the top of the pan with your rolling pin.
Cut a piece of baking parchment to fit the pan, lay on the pastry and weigh down with dried beans. Bake in a preheated oven (200°C/400°F) for 20 minutes, then take out of the oven and remove the baking parchment and dried beans.
Meanwhile, beat the eggs and sugar in a metal bowl until thick and foamy. Stir in the creme double, lemon juice and grated lemon peel and add the butter in small flakes. Then beat over a hot bain-marie with an electric beater until thick and creamy. Finally stir in the ground almonds.
Drop the peaches into boiling water for a few seconds, then skin, halve, remove the pits and slice thinly.
Spread the almond filling smoothly in the hot pastry shell, arrange the peach slices attractively on the filling and bake in a preheated oven (180°C/350°F) for about 45 minutes, until the filling is set.
It should be lightly browned, but cover with aluminum foil if it browns too quickly. Take out of the oven and let cool.
Remove from the oven and let cool on a wire rack. Serve warm or at room temperature with a garnish of basil.