Heat the oven. Preheat the oven to 425°F (220°C).
Lightly flour your work surface and roll the pie crusts to a thickness of 1/8 inch. Cut out 12 circles using a 3.5-inch cookie cutter or a cup. Re-roll the leftover pieces of dough as necessary to get all 12 circles.
Place one dough circle into each cavity of a standard 12-count muffin pan. Gently press the dough against the bottom and sides so that it fits snugly inside each cavity. Put the muffin pan and any remaining pie dough in the refrigerator while preparing the filling.
Add the chopped apples, granulated sugar, all-purpose flour, ground cinnamon, vanilla extract, and ground nutmeg to a large mixing bowl. Stir until everything is thoroughly combined and the apples are evenly coated.
Take the muffin pan out of the refrigerator. Divide the apple mixture evenly among the 12 crusts, using about 3 tablespoons of filling for each pie.
If using the optional butter, cut the tablespoon of butter into 12 small pieces. Place one piece over the filling in each pie.
Take the reserved pie dough from the refrigerator. Cut the dough into your preferred decorative shapes and arrange them over the tops of the pies.
Bake for 18 to 23 minutes. The pies are ready when the crust has turned lightly golden brown and the apple filling is bubbling.
Remove the muffin pan from the oven and allow the pies to cool in the pan for 10 to 15 minutes. Carefully lift each mini pie from the pan and place it on a wire rack to finish cooling.