For the crumb topping: In a medium bowl, mix the flour, brown sugar, granulated sugar, cinnamon, nutmeg and salt using a fork or pastry cutter. Cut the butter into small pieces and gradually add it to the flour mixture until evenly mixed. Set aside.
For the apple filling: In an 8-inch cast-iron skillet, heat the butter over medium heat. Add the apple slices and a pinch of salt and cook for 3 minutes. Stir in the brown sugar, cornstarch, vanilla and lemon juice.
Cover the apple filling in the skillet evenly with the crumb topping. Cover with foil and bake for 15 minutes. Remove the foil and bake until crisp and brown on top, an additional 20 to 30 minutes.