In a medium bowl, combine the diced peaches, granulated sugar, brown sugar, cinnamon, nutmeg (if using), and lemon juice. Stir in the cornstarch mixture and set aside to thicken while you prepare the dough.
In a large bowl, whisk together the flour, salt, and baking powder. Using a pastry cutter or your fingers, cut in the cold butter until the mixture resembles coarse crumbs.
Gradually add the buttermilk, stirring gently until a soft dough forms. Be careful not to overmix.
Turn the dough onto a floured surface and roll it out to about 1/8 inch thickness. Use a round cutter (about 4 inches in diameter) to cut circles from the dough.
Spoon about 1 tablespoon of the peach filling onto one half of each dough circle. Fold the dough over to form a half-moon shape and press the edges together to seal. Crimp the edges with a fork.
Heat vegetable oil in a deep skillet or fryer to 350°F (175°C). Fry the pies in batches for 2-3 minutes per side, or until they are golden brown and crispy.
Remove the pies from the oil and drain on paper towels. Dust with powdered sugar before serving.
