Fried Apple Pies

Blend together flour, butter, shortening, baking powder, and salt in a bowl with your fingertips or a pastry blender (or pulse in a food processor) until mixture just resembles coarse meal. Whisk egg with 1/4 cup ice water, then drizzle evenly over flour mixture and gently stir with a fork until incorporated.
Squeeze a small handful: If it doesn't hold together, add more ice water, 1/2 tablespoon at a time, stirring (or pulsing) until incorporated.
Gather dough and knead just until smooth, 3 or 4 times, on a lightly floured surface (do not overwork, or pastry will be tough). Form dough into 2 (5-inch) disks and chill, wrapped in plastic wrap, until firm, at least 1 hour.
Briskly simmer all filling ingredients and a pinch of salt in a heavy medium saucepan, uncovered, stirring occasionally and mashing apples with a potato masher as they soften, until a thick purée forms, about 20 minutes. Cool completely.
Divide 1 disk of dough into 6 equal pieces. Roll out 1 piece on a lightly floured surface with a lightly floured rolling pin into a 6-inch round, then put 2 heaping tablespoons of filling in center. Lightly moisten edge with water and fold dough over to form a half-circle, pressing out air around filling, then pressing edge to seal. Transfer to a large sheet of parchment paper and press floured tines of a fork around edge. Make more pies with remaining dough and filling (you may have some filling left over).
Set a cooling rack on a large baking sheet or tray. Heat 2 inches of oil in a 4- to 5-quart heavy pot (preferably cast-iron) over medium heat until it registers 360 to 370°F on thermometer. Fry pies, 3 or 4 at a time, turning occasionally, until deep golden-brown, 7 to 8 minutes per batch. Transfer to rack to drain. Return oil to 360 to 370°F between batches.
Dust warm pies with confectioners sugar before serving.