Preheat oven to 325 degrees. Grease two 8-9 inch round baking pans. Line ONE of them with parchment paper (this one will not have caramel apples).
In a small sauce pan melt 1/4 cup butter over medium heat. Add in the 2/3 cup of brown sugar. Bring to a boil while stirring. Remove from heat and stir in the 1/2 tsp of cinnamon. Pour caramel into one of the greased baking pans (the one without parchment). Arrange apple wedges in the caramel overlapping slightly, until the pan is covered in apples. Set aside while cake comes together.
In a medium bowl, combine flour, baking powder, cinnamon, and salt. In a separate mixing bowl or stand mixer beat sugar and butter until combined. Beat in eggs one at a time, and add the vanilla. Gradually add in some of the flour mixture and the milk, alternating until all is combined and smooth. Spread half the batter over the apples, and the other half in a very well greased and lined second round baking pan.
Bake the cake with the apples for 50-55 minutes. Bake the cake without apples for 40-45 minutes, or until toothpick comes out clean for both. Let cool in the pan on a cooling rack for 15 minutes. Run a knife around the edges and turn over onto a flat plate or large cutting board. Let both cakes cool completely.
Using a mixer beat together powdered sugar, butter, caramel sauce and vanilla. Start by adding 2 tbsp milk. Use more if frosting seems too thick. Mix in kosher salt. NOTE: if you are using table salt, start with 1/8 tsp and taste before adding more.
Place cooled bottom layer of cake onto a serving platter. Spread desired amount of buttercream onto the cake (almost all but about 1 cup). Drizzle some caramel topping on top of the buttercream. Place the caramel apple cake on top of the frosted bottom cake, apples side up. Smooth out the frosting around the edges, add more to the edges if needed, cake should look rustic! Drizzle more caramel topping around the edges to get the drip look.
If you do not want to make the double layer cake, you can make just the single apple upside down cake. Just as impressive and delicious! You would just cut the cake section of the recipe in half to make one round or square cake. The caramel apple ingredients stay the same, and you wouldn't make the buttercream.
The caramel sauce used in the buttercream and decorating drips is store bought, but if you like to make your own dessert caramel sauce for that part as well, go for it!