Preheat over to 350 coat sheets with cooking spray or line with parchment paper set aside
Peel and dice apples up, Place in saucepan with sugar cinnamon and nutmeg over low-medium heat. Stir constantly until apples are soft, about 10-12 minutes. Remove from heat and set in refridgerator to cool.
In a medium mixing bowl, combine flour and salt. Cut in the shortening until pieces are the size of small peas. Add water to slightly moisten. Form dough into a ball.
On a lightly floured surface roll out the dough to about 1/8 inch thick and using a 3 1/2-inch to 4-inch round cookie cutter, cut out dough circles. Take the dough scraps, work them together, reroll, and cut out as many circles as possible.
Whisk together the egg and water to make an egg wash. Place a large spoonful of the apple mixture in the center of each dough circle. Using a pastry brush, lightly brush the egg wash around the edge of half of each circle of dough, about 1/3-inch from the edge. Fold the dough over the filling so that the edges meet and using the tines of a fork, press the edges together.
Arrange the empanadas 2 inches apart on prepared cookie sheets. Lightly brush tops of empanadas with egg wash. Bake in preheated oven for 17-20 minutes, or until lightly browned. Remove the empanadas from oven and let them sit at least 5 minutes before serving.