Combine all-purpose flour, granulated sugar, and salt in a food processor. Cut in cold unsalted butter until pea-sized crumbs form. Gradually add cold water, pulsing until the dough comes together. Shape into a disc, wrap in plastic wrap, and chill for at least 1 hour.

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

Slice peaches and combine with light brown sugar, cornstarch, and vanilla extract in a bowl. Allow to rest for 10 minutes.

Roll out the dough into a circle ⅛ inch thick. Transfer to the baking sheet. Spoon peach mixture into the center, leaving a 3-inch border. Fold edges over filling and pinch to seal.

Brush crust with beaten egg and sprinkle with almond slices. Bake for 25-28 minutes until golden brown and bubbly.

Cool for at least 15 minutes before slicing and serving.