1. Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper.
2. In a mixing bowl, combine flour, sugar, and salt. Add cold butter and mix until the mixture resembles coarse crumbs.
3. Gradually add ice water, mixing until the dough comes together. Form into a disk, wrap in plastic, and refrigerate for 30 minutes.
4. In another bowl, toss peach slices with sugar, lemon juice, and cornstarch.
5. Roll out the dough on a floured surface into a 12-inch circle. Transfer to the prepared baking sheet.
6. Arrange the peach slices in the center of the dough, leaving a 2-inch border. Fold the edges over the peaches, pleating as needed.
7. Brush the dough edges with the beaten egg.
8. Bake for 40 minutes or until the crust is golden and the peaches are tender. Let cool before serving.