Peel, core and chop the apples into small pieces. Melt the butter in a 10-12 inch fry pan. Cook the apples over medium heat for about 15-20 minutes or until soft. Sprinkle with brown sugar and sugar while they cook. Stir with a wooden spoon occasionally, making sure they do not burn. Sprinkle with cornstarch once they are almost done and let cook to thicken the apples and juice.
Remove from the heat and add the cinnamon, nutmeg and stir to combine. Let the pie filling cool completely.
Roll out your biscuit dough or pie crust on a lightly floured surface, into 4-6 inch ovals, about 1/8-1/4-inch thick. Scoop about 1 tablespoon or so of the cooled pie filing in the center of each round. Fold over, lightly press down on the filling and the edges. (Lightly wet edges with water, using your fingertip if needed) Crimp the edges of the dough with a floured fork. Place uncooked pies on a half-sheet pan which is lined with parchment paper.
Fill a fry pan with about 2-3 inches of canola oil. Heat the oil until very hot. Place only a few hand pies in the hot oil at a time, as to not overcrowd the pan or let the oil cool. Fry until they are brown on both sides, about 3-4 minutes. Remove from the hot oil and let drain on paper towels on a half-sheet pan. Sprinkle with granulated sugar or dust with powdered sugar while they are still warm. These are best served warm.