Prepare your work area by preheating your oven to 375°F (190°C) and lining a baking sheet with parchment paper.
Make the filling by combining the diced apples, granulated sugar, brown sugar, flour, cinnamon, nutmeg, salt, lemon juice, and vanilla in a mixing bowl. Stir well to ensure the apples are evenly coated, then set aside for 10 minutes to allow flavors to meld.
Roll out the pie crusts on a lightly floured surface to about 1/8-inch thickness. Using a 5-inch round cutter or bowl as a guide, cut out as many circles as possible (you should get about 8 circles from the two crusts).
Place about 2 tablespoons of apple filling slightly off-center on each dough circle, leaving at least a 1/2-inch border around the edges. Be careful not to overfill or the pies may leak during baking.
Create the hand pies by folding each circle in half over the filling to create a half-moon shape. Press the edges firmly to seal, then crimp with a fork or fold over to create a decorative edge.
Transfer the pies to the prepared baking sheet, spacing them about 2 inches apart. Cut a small vent in the top of each pie to allow steam to escape during baking.
Make the egg wash by beating the egg with 1 tablespoon of water in a small bowl. Brush the tops of each pie with the egg wash, then sprinkle with coarse sugar if using.
Bake for 20-25 minutes or until the pies are golden brown and the filling is bubbling through the vents. Rotate the baking sheet halfway through to ensure even browning.
Allow the pies to cool on the baking sheet for 10 minutes before transferring to a wire rack to cool completely (or enjoy them warm for a gooey filling).