1-Prepare the crust: Prepare the crust by pulsing 1 1/3 cups all-purpose flour, 1 tablespoon granulated sugar, and 1/2 teaspoon salt in a food processor. Add 8 tablespoons of very cold unsalted butter cut into cubes and pulse until the mixture resembles pea-sized pieces. Add 6 tablespoons of ice water one tablespoon at a time, pulsing until the dough clumps together, then form it into a disk, dust with flour, cover with plastic wrap, and refrigerate for at least 1 hour or up to 3 days.

2-Preheat and roll: Preheat the oven to 425°F (220°C). On a floured surface, roll the dough into a 12-inch circle and transfer it to parchment paper on a rimmed baking sheet, then chill it while you make the filling.

3-Mix filling ingredients: In a bowl, mix 1/4 cup granulated sugar, 1 tablespoon all-purpose flour, and 1/2 teaspoon cinnamon. Slice the peaches and toss them with the sugar mixture and 1/2 teaspoon vanilla extract.

4-Arrange peaches: Arrange the peaches in a circular pattern on the dough, leaving a 2-inch border, then drain any excess juices and dot the peaches with small pieces of 1/2 tablespoon unsalted butter.

5-Fold dough: Fold the dough edges over the peaches, pinching to seal.

6-Brush and sprinkle: Brush the crust with the beaten egg and optionally sprinkle with 1 tablespoon turbinado sugar.

7-Bake and cool: Bake for 25 to 30 minutes until the crust is golden and the juice is syrupy, then let it cool for 15 minutes before serving. Remember, the total preparation time is about 1 hour 20 minutes for prep and chilling, with 20 30 minutes for baking, making the whole process around 2 hours.