Core, peel and dice 2 of the apples. Cut the tops off of the other apples. Then use a melon baller to hollow out the inside of each apple.
Place hollowed out apples into a baking dish sprayed with non-stick cooking spray.
Combine cornstarch and 1 tablespoon water in a small bowl and stir until dissolved. Add apple pieces, cornstarch mixture, 1/2 cup sugar and 1 teaspoon cinnamon to a pan. Cook over medium heat stirring constantly for 10 minutes. Reduce heat to low and simmer for 5 minutes. Remove from heat.
Allow filling to cool for a few minutes to thicken up, then fill each apple.
Flatten out pie crust then cut into 1/4 inch strips. A pizza cutter is a great tool for this! The strips need to be just long enough to go across the apples. Place strips in a lattice pattern atop each apple.
Whisk together egg and a little water (about a teaspoon) to make an egg wash. Brush the crusts with the egg wash.
Combine 1/4 cup sugar, 1 teaspoon cinnamon and nutmeg and mix well. Then sprinkle sugar mixture over the crusts.
Bake apples for 30 minutes at 375 degrees or until crust is brown and filling is bubbly.
Top with with caramel sauce drizzle right before serving, if desired.