Preheat the oven to 350° and rub some butter all around an 8-inch skillet all around the bottom and up the sides.
To make the cake:
Beat butter and sugar in a bowl of an electric mixer for a couple of minutes.
Start adding the eggs one at a time, while sugar and butter are beating. Once eggs are incorporated, stop and scrape sides and bottom of the bowl.
On low speed, stir in flour, baking powder, and spices.
Once combined, raise the speed a little and pour in vanilla extract and buttermilk. Mix until just combined.
Scrape sides and bottom of the bowl and give it a quick stir.
Fold in the diced apples with a spatula.
Spread the batter in the prepared skillet evenly and bake for 35-40 minutes.
Topping:
Peel, core, and slice apples thinly.
Melt butter in a medium sauce pot and add apples and brown sugar. Mix well and let apples simmer over medium heat. Let them simmer for 15-17 minutes but make sure to stir every few minutes.
One apples are soft and about half of the liquid has evaporated, set the sauce pot aside.
When cake it done, take it out of the oven and spread apples and sauce all over the top and let it drip off to the sides. (It will be delicious soaked in!)
Sprinkle a little sea salt on top if you wish and drizzle some caramel topping.