Place the apples into a saucepan with the sugar and cinnamon, and bring to a simmer over low heat. Cook the apples, stirring frequently, until soft, about 10 minutes; mash the apples with a fork to form a chunky applesauce. Set the apple filling aside.
Whisk flour and salt together in a bowl, and cut in the shortening with a pastry cutter until the mixture resembles coarse crumbs. Stir in water until the dough is moistened, and knead several times just until dough holds together. Place dough onto a floured surface, pat into a round, and roll out 1/8-inch thick. Use a large round cookie cutter (4 inches in diameter) to cut the dough into 8 rounds.
Place a heaping tablespoon of apple filling onto the center of a dough round, and use your finger to moisten the edge of the crust with cold water. Fold the dough over the filling, and crimp the edges with a fork to make a half-moon-shaped pie. Repeat with remaining dough and filling.
Pour the oil into a skillet over medium-high heat, and gently lay 2 or 3 pies into the hot oil. Fry to a golden brown color, 2 to 3 minutes per side. Drain the pies on paper towels. Sprinkle a pinch of confectioners' sugar over each pie to serve. Allow to cool for at least 10 minutes before serving.
