In a mixing bowl, combine flour, sugar, and salt. Add the cold cubed butter and mix until the mixture resembles coarse crumbs.

Gradually add ice water, mixing until the dough comes together. Form into a disk, wrap in plastic, and refrigerate for at least 30 minutes.

In another bowl, combine sliced peaches, brown sugar, cornstarch, vanilla extract, and lemon juice. Toss to coat the peaches evenly.

Preheat the oven to 375°F (190°C). Roll out the chilled dough on a floured surface into a 12-inch circle.

Transfer the dough to a baking sheet lined with parchment paper. Spoon the peach filling into the center, leaving a 2-inch border.

Fold the edges of the dough over the filling, pleating as necessary. Brush the dough with the beaten egg.

Bake in the preheated oven for 30-35 minutes, or until the crust is golden brown and the peaches are bubbly.

Allow to cool slightly before serving. Enjoy warm or at room temperature.