Preheat the oven to 350 degrees F (180 degrees C).
Peel and chop the apples into small pieces. I like to chop them up very well so that they cook quickly and evenly in the pan.
Melt the butter in a pan on medium-low heat and add in the apples, cinnamon, and maple syrup.
Mix the apples to coat and reduce the heat to low. Cover the pan and let the apples cook for about 10 minutes (stirring occasionally). If your apple mixture seems dry, add in a little more melted butter.
Once the apples are softened and cooked, set them aside to cool. You want the apples to be tender, but not too mushy as they will continue to cook in the oven.
Unroll the pie crust on a floured surface and use a cookie cutter (about 2-2.5 inches in diameter) to cut out 12 circles. Set the scraps aside to use for the top layer of the mini pies.
Combine the scraps and re-roll the dough out. Use a pizza slicer or knife to cut out thin strips about 3 inches in length.
Place about 1 tablespoon of the apple mixture into the center of each circle. Place two crust strips horizontally and another two crust strips vertically over each mini pie. Press down on the sides and use a fork all around the edges of each pie to seal the crust in place.
Whisk together 1 egg and 1 tablespoon of water for the egg wash and brush this mixture on top of each pie.
Bake the pies for 15 to 18 minutes, or until golden brown.