Place your oven rack in the middle of the oven and preheat oven to 350ºF.
Prepare the topping, melting the 1/3 cup butter in a 10 cast iron skillet ((2 deep), over low heat.
Remove skillet from heat and stir in the brown sugar and ground cinnamon (or apple pie spices) using a fork.
Spread this mixture evenly over the bottom of the skillet and arrange the apple slices over the butter/sugar mixture in the skillet.
In a mixer, blend cake mix, 1 stick melted butter, sour cream, dark corn syrup, eggs and ground cinnamon.
Beat on low speed for 1 minute. Increase speed to medium and beat 2 minutes longer until creamy.
Pour the batter over the top of the apples in the skillet and then place the skillet in the oven and bake at 350ºF. for 40-45 minutes and bake until the cake rises high in the skillet, (it will spring back when lightly pressed with your finger when it's done).
Remove skillet and cool cake in the pan for 5-10 minutes and then run a knife around the edges of the cake to loosen it from the sides of the pan and carefully flip upside down onto a serving plate.
Cool completely for about 15 minutes and serve warm with vanilla ice cream if you like.
I have made this cake with Duncan Hines Caramel flavor cake mix and the taste is excellent, too.
NOTE: this cake can also be made in these baking pans. Just prepare the butter, brown sugar and spices in a skillet over the stove and then pour this mixture in the baking pan sprayed with cooking oil, add the apple slices, pour the batter and bake it.
Here is a guide to bake the cake in those pan sizes: