Preheat oven to 375°F (190°C). Line a baking sheet with parchment paper.
In a mixing bowl, combine flour and salt. Cut in cold butter until mixture resembles coarse crumbs. Gradually add ice water, mixing until dough comes together. Divide dough in half, shape into disks, wrap in plastic, and refrigerate for at least 30 minutes.
In another bowl, combine peaches, sugar, lemon juice, cornstarch, and vanilla extract. Set aside.
On a floured surface, roll out one disk of dough to about ⅛-inch thickness. Cut out circles using a 4-inch cutter. Repeat with the second disk of dough.
Place a spoonful of peach filling in the center of each dough circle. Fold dough over filling to create a half-moon shape. Press edges with a fork to seal. Place on prepared baking sheet.
Brush each pie with beaten egg and sprinkle with coarse sugar. Cut small slits on top for steam to escape.
Bake for 20-25 minutes or until golden brown. Let cool slightly before serving.