1. Add the peaches, granulated sugar, brown sugar, lemon juice, vanilla extract, cinnamon, and nutmeg to a saucepan over medium heat. Cook for 4 to 5 minutes, stirring often, until the peaches soften.

2. Stir together the cornstarch and 2 tablespoons water in a small bowl. Add the slurry to the peach mixture and cook for 1 to 2 minutes until thickened. Stir in the butter and let the filling cool completely.

3. Roll out the pie crusts and cut into 4 to 5 inch circles.

4. Whisk the egg with 1 tablespoon water. Spoon a small amount of cooled filling into the center of each dough circle. Brush the edges with egg wash, fold over, and crimp with a fork to seal.

5. Chill the assembled pies for 15 to 20 minutes.

6. Heat 2 to 3 inches of vegetable oil in a deep skillet or pot to 350°F.

7. Fry the pies in batches for 2 to 3 minutes per side until golden brown and crisp.

8. Transfer to a paper towel-lined plate or wire rack.

9. Dust with powdered sugar and serve warm.