Preheat the oven to 350°F and grease a 13 x 9 inch pan very well with baking spray or softened butter, coating the corners and sides so the topping releases cleanly.
Peel your apples and thinly slice them.
Melt the butter and pour it into the bottom of the prepared pan and tilt to cover the surface evenly.
Mix together the brown sugar, cinnamon, nutmeg and salt in a bowl. Then, sprinkle the brown sugar mixture evenly over the melted butter in the pan.
Arrange the thinly sliced apples over the brown sugar in an even layer, allowing slight overlap but avoiding thick stacks so the apples cook through.
In a large bowl, prepare the yellow cake mix according to package directions using the eggs, oil, and water. Stir in vanilla and extra cinnamon if desired.
Carefully spoon or pour the cake batter over the apples, spreading gently into an even layer without shifting the apple slices too much.
Bake for about the time specified on your cake mix for a 9x13 pan, or until the center is set and a toothpick inserted into the cake portion comes out clean or with a few moist crumbs.
Cool the cake in the pan on a wire rack for 10 to 15 minutes. Do not let it cool completely or the caramel may stick too firmly.
Run a knife around the edges, place a serving platter or sheet pan on top of the cake pan, then flip the whole thing over. Let it sit for 1 to 2 minutes, then lift the pan to reveal the apple topping.
If any apples stay behind, reposition them with a spatula and spoon any extra caramel from the pan back over the apples. Serve warm or at room temperature with whipped cream or vanilla ice cream if you like. Store leftovers covered in the fridge and reheat individual slices in the microwave.