Prepare pie crust and refrigerate for 1 hour. Pull from fridge and let rest on the counter for 10 minutes so they will roll out more easily. Line a baking sheet with parchment paper. Heat the oven to 425 degrees.
While the oven heats, peel, core, and dice the apples. Melt the butter in a large skillet over medium-high heat. When butter is melted, add the apples, brown sugar, cinnamon, nutmeg and salt, and cook for 5-10 minutes over medium heat, stirring occasionally, until apples have softened and released their juices.
Sprinkle the flour over the apples and stir thoroughly to combine. Cook for 1 minute more to thicken the juices released from the apples, then remove from heat.
Roll out 1 crust on a lightly floured surface and cut it into apple shapes with an apple cookie cutter, or use a large circle cutter. Gently transfer the apple-shaped pieces of crust to a parchment lined backing sheet. You may need to combine and re-roll scraps of pastry dough.
Scoop 1 tablespoon of apple pie filling into the center of each apple crust, leaving space on the edges to seal with a second crust. Roll out the second crust on a lightly floured surface and cut it into apple shapes with the same cookie cutter or large circle cutter. Carefully place each top crust on each mound of apple pie filling and press the sides down to match the sides of the bottom crust. You may need to slightly stretch the top crust to reach the edges. Use a fork to press around the edges of each hand pie for a good seal and a decorative finish.
Make an egg wash by beating the egg in a small bowl with 1 teaspoon of water, then brush the tops of each hand pie with the egg wash using a pastry brush. Cut a slit in the dough on top of each hand pie.
Bake at 425 degrees for 18-20 minutes, until the crust is lightly browned. While the hand pies are baking, prepare glaze by whisking together the powdered sugar and milk in a medium bowl.
When pies are done, transfer them to a wire rack and brush with the glaze using a clean pastry brush. Alternatively, you could drizzle the glaze over the pies or even dip them into the glaze. Allow to cool and let the glaze set for at least 10-15 minutes before serving either warm, cold or room temperature.