Preheat oven to 200°C. Roll out the dough and spread in a shallow large form or on a baking sheet so that you get the sides. Sprinkle the dough with vanilla sugar.
Wash the peaches and remove the pits, cut into slices 5–7 mm thick.
Lay the peaches on the dough with an overlap, sprinkle with brown sugar. Spread the oil cut into thin “petals” on top.
Place the pie in the oven and bake until golden brown on the peaches, about 35 minutes. Serve hot, you can add a scoop of ice cream.