In a medium bowl, mix flour and salt; cut in shortening until crumbly. Stir in water until completely moistened. Divide pastry into 2 equal portions. Roll out each portion thinner than you would for pie crust. Cut into circles with a 3-1/2" biscuit or cookie cutter.
In a medium saucepan, simmer diced apples, cider, sugar, cinnamon, and nutmeg over low heat until apples are soft. In a small bowl, mix cornstarch with enough water to form a thin consistency; stir into apple mixture and cook until mixture thickens.
Assembly and cooking:
Brush pastry circles with beaten egg. Place a small spoonful of apple mixture in center of each circle. Fold pastry over filling to form a half circle. Press edges together with a fork to seal.
Heat 1 cup of cooking oil to 400 degrees in an electric skillet. Place several empanadas in hot oil at a time, cooking on one side, and turning over when golden brown. Cook second side until golden brown. Remove and drain on paper towels.
Sprinkle tops of empanadas with cinnamon and sugar mixture.