In a large skillet over medium heat, melt the butter. Stir in the apples, sugar, and salt and cook/simmer, stirring occasionally, until apples are softened a bit, about 5 minutes. Transfer to a bowl to cool completely (stick it in the freezer to speed things up and stir every 10 minutes, we don’t want them warm!).
Preheat the oven to 350F. Generously grease a 10-inch cast-iron skillet with some butter.
In a large bowl, whisk together the melted butter, sugar, eggs, and vanilla until smooth.
In a separate bowl, mix together the flours, baking powder, cinnamon, and salt.
Add the dry ingredients to the wet ingredients and use a rubber spatula to gently fold it in until most of the flour is mixed in. Fold in your room temp caramel apple mixture until just combined, making sure to incorporate all that caramel apple liquid.
Transfer the batter to your prepared skillet, spread into an even layer and bake for 25-30 minutes or until it feels firm in the center, then broil for 1-2 minutes just to brown the top (keep an eye on it the whole time!).
Enjoy the cake warm or at room temperature served with ice cream or whipped cream.