Mix sugar, flour, cinnamon, and nutmeg together in a bowl. Mix in apple slices.
Place 1 pie crust in a 10-inch deep-dish pie plate. Add the apple mixture, gently pressing to pack in the filling. Dot with butter. Cover with the top pie crust and finish edges to your liking. Cut slits into the top crust. Place pie plate on a baking sheet.
Bake in the preheated oven until golden brown, about 1 hour.
Heat condensed milk in a saucepan over medium heat. Stir constantly, until caramel forms, about 15 minutes. Pour caramel sauce over the hot pie.