Preheat oven to 350F and lightly grease a 9-inch cast iron skillet.
In a medium pan over medium heat, saute the diced apple with 1 tablespoon butter, 1 tablespoon brown sugar, and cinnamon for 5 minutes until soft. Set aside.
In a large bowl, cream the butter, brown sugar, and granulated sugar until fluffy, then mix in the egg and vanilla.
Add the gluten-free flour, baking soda, and salt, mixing until a soft dough forms. Fold in half of the cooked apples.
Press the dough evenly into the skillet, top with the remaining apples, and bake for 20 to 25 minutes.
Drizzle the baked cookie with caramel sauce while still warm and serve.