In a food processor, combine flour, granulated sugar, and salt. Cut in cold butter until mixture resembles coarse crumbs. Gradually add cold water until dough forms a ball. Wrap in plastic wrap and refrigerate for at least 1 hour.

Preheat your oven to 425°F (190°C) and line a baking sheet with parchment paper.

In a mixing bowl, combine sliced peaches, brown sugar, cornstarch, and vanilla extract. Toss until peaches are coated.

On a lightly floured surface, roll out the chilled dough into a circle, about ⅛ inch thick. Transfer to the prepared baking sheet.

Spoon the peach filling into the center of the dough, leaving a 3-inch border. Fold edges of dough over peaches.

Brush edges of dough with beaten egg and sprinkle almond slices over the crust.

Bake for 25-28 minutes until crust is golden and filling is bubbling.

Cool for at least 15 minutes before slicing and serve warm.