In a medium bowl, stir together the sugar and cocoa powder. Add the melted butter and stir until the mixture forms a paste. Set aside while you prepare the dough.
In a medium bowl, combine the flour and salt. Cut up the shortening with a long-tined fork. Add the milk and stir until the dough sticks together. Divide into 10 portions. Roll each portion out on a floured surface into a 5-of-6-inch circle. Place 2 tablespoons of filling in each. Wet the edges and fold over, crimping with a fork. In a large skillet, pour the oil to a depth of 1/4-inch and heat over medium heat. Place the chocolate pies in the hot oil and fry until browned on both sides, turning as needed. Remove to a paper towel-lined plate. You can put to sprinkle powdered sugar on chocolate fried pies if you like.