Working around the core, cut off the cheeks of the apples. Slice the apple cheeks very thin. Place all the apple slices in a large mixing bowl.
In a medium mixing bowl, combine sugar, brown sugar, cinnamon, and nutmeg. Stir to combine. Pour the cinnamon-sugar mixture over the apple slices and stir to coat, then let sit for 30 minutes.
After 30 minutes, remove the apples from the cinnamon-sugar mixture and squeeze them with your hands to remove the excess moisture. Place the drained apples in a separate bowl, reserving the liquid to make the caramel sauce.
Preheat the oven to 375 degrees F.
Place one sheet of pie crust in the bottom of a 12" cast iron skillet. Cut the other sheet of pie crust into strips and press them into the walls of the skillet attached to the bottom pie crust. Use a fork to poke holes in the bottom pie crust. Bake for 15 - 20 minutes.
While the crust is baking, bring the reserved cinnamon-sugar mix to a boil in a medium saucepan. Once the liquid is reduced by half (around 10-15 minutes), add the heavy cream and stir thoroughly. This is your caramel sauce.
Pour about 2 tablespoons of the caramel sauce in the baked pie crust.
Starting from the outside and working your way in, place the apple slices on the pie crust and slightly overlap them as you begin to layer to create a rose shape. Roll 1 to 2 thinly slices apples up tightly and place in the center.
Pour the remaining caramel sauce over the roses.
Cover the cast iron skillet with foil, and bake for 35-40 minutes. Uncover and bake for an additional 10 min.
Serve warm and enjoy with ice cream!