Preheat the oven to 400°F (204°C). Line 1 to 2 large baking sheets with parchment paper or silicone baking mats and set aside.
On a lightly floured surface, roll the pie crusts to about 1/8-inch thick. Using a 3.5-inch cookie cutter (or cup) cut out as many circles from the pie crusts as you can, reroll any scrap pieces of dough as needed. You should get about 18 to 20 circles. Place the cut-out pie crust circles on the baking sheets and transfer to the refrigerator to chill while you make the filling.
Combine the chopped apples, sugar, flour, vanilla extract, ground cinnamon, and ground nutmeg in a mixing bowl until fully combined and all of the apples are coated with the mixture.
In a separate bowl, whisk together the egg and milk until well combined. Set aside.
Remove the pie crust circles from the refrigerator and evenly distribute the apple pie filling between half of them, making sure to leave some room at the edges. Place 1 to 2 pieces of the cubed butter on top of the filling on each pie.
Place the other half of the pie crust circles on top (use some water or the egg wash to dampen the edges and help seal them together if needed) then crimp the edges with a fork.
Brush the top of each pie with the egg wash. Sprinkle with coarse sugar if desired, then cut 2 to 3 slits in the top of each pie.
Bake for 18 to 22 minutes or until the pies are golden brown and the filling is bubbling. Remove from the oven and set aside to cool slightly before serving.