Make the apple pie filling: In a small bowl combine cornstarch and water until dissolved. In a medium saucepan, over medium heat, combine cornstarch slurry, apple pieces, sugars, cinnamon, nutmeg, allspice, and vanilla extract. Cook for 5 minutes, stirring constantly, then reduce heat to low and let simmer for 5 minutes. Remove from heat and let cool for 20 minutes.
Preheat oven to 375℉ (190℃) and grease a 12-count muffin pan.
Make mini crusts: On a floured work surface, roll each pie crust into a large 12-inch circle. Cut the dough into twelve 3.5-inch circles with a cookie cutter or equally sized measuring cup. Place the dough rounds into the greased muffin pan by pressing it flat into the bottom of the crevice and up the sides. Put the muffin pan in the fridge. Roll out any leftover pie crust and cut into ¼-inch wide strips using a pizza cutter or knife. You need 6 strips for each pie. The strips should be slightly longer than the mini pies. Put strips on a cutting board and chill until apple pie filling has cooled down.
Lattice crust: Make a large lattice crust on the cutting board, then cut out crusts with a cookie cutter the same size as the muffin pan openings. This way the crusts look neater.
Assemble: When the pie filling has cooled down, evenly spoon it into each crust. Carefully put a mini lattice crust on each mini pie and gently press the edges together to secure the lattice crust.
Finish: Whisk the egg and milk together. Lightly brush the tops with egg wash and sprinkle with coarse sugar.
Bake the mini apple pies for about 25-30 minutes until the crust is golden brown. Allow to cool for 5 minutes before removing them from the pan. Let cool on a wire rack. Serve with whipped cream, vanilla ice cream, or caramel sauce.