Preheat your oven to 425°F. Line a baking sheet with parchment paper.
In a medium bowl, combine the diced peaches, granulated sugar, lemon juice, cinnamon, and cornstarch. Stir until the peaches are well coated and set aside to let the mixture thicken for about 10 minutes.
Roll out one pie crust on a lightly floured surface. Use a round cutter or a glass to cut out circles, about 4 inches in diameter. Repeat with the second pie crust.
Place a heaping tablespoon of the peach filling in the center of each circle. Fold the dough over to create a half-moon shape and press the edges to seal. Use a fork to crimp the edges for a decorative touch.
Transfer the hand pies to the prepared baking sheet. Brush the tops with the beaten egg and sprinkle with coarse sugar.
Bake for 20-25 minutes or until the hand pies are golden brown. Remove from the oven and let cool for a few minutes before serving.