Place flour, sugar, salt, and butter in a food processor and pulse for a few seconds. Larger butter flakes should be still visible.

Add one tablespoon water at the time and pulse for 1-2 times after every tablespoon. Form pie crust into a disc without kneading. Wrap in plastic foil tightly. Refrigerate for at least 1 hour up to 2 days.

Preheat oven to 425°F (190°C). Line a large baking sheet with parchment paper. Set aside.

In a large mixing bowl, stir peaches, sugar, cornstarch, and vanilla to combine. Set aside.

Roll out dough into a 1/8 inch thick circle and transfer to the prepared baking sheet. Spoon peaches without any liquid in the center of the dough, leaving a 3-inch border all around.

Fold edges over peaches and press gently to seal the edges. Brush edges with egg, and sprinkle with almond slices.

Bake for about 25-28 minutes. Allow cooling at least 15 minutes before slicing and serving.