Cook the apples, butter, brown sugar, cinnamon, and lemon juice in a skillet over medium heat for 6 to 8 minutes, until slightly softened.
Mix cornstarch with water, then stir it into the apples. Cook for 1 minute until thickened, transfer the filling to a bowl, and cool completely.
Preheat the oven to 400°F or 200°C. Roll out the pie crusts and cut sixteen circles using a 4-inch cutter or a small bowl.
Place filling in the center of eight circles, leaving a clean border. Brush the edges with water and place the remaining circles on top.
Crimp the edges with a fork and cut small vents in each pie. Whisk the egg with milk, brush the tops, and add coarse sugar if desired.
Bake on a parchment-lined sheet for 18 to 22 minutes. Cool for at least 10 minutes because the filling will be extremely hot straight from the oven.
