Make the cake: Preheat the oven to 400°F. Butter or oil a 10-by-15-inch jellyroll pan or a 16-3/4 by 12-inch sheet pan.

In a large bowl, combine the flour, baking soda, salt, granulated sugar, brown sugar, and cinnamon.

In a medium saucepan over medium-high heat, combine the butter with 1 cup water and heat until the butter melts. Bring to a boil. Once the mixture is boiling, remove from heat and add in the flour mixture. Add in the buttermilk, eggs, and vanilla. Gently stir in the apples.

Pour the batter into the prepared pan, spreading evenly. Bake for 20 minutes if using a jelly roll pan, and about 17 minutes if using a half sheet pan, or until a toothpick inserted comes out clean. Let cool in the pan on a wire rack for about 10 to 15 minutes.

Make the frosting: Meanwhile, combine the butter and milk in a large heat-proof bowl. Microwave until the butter is melted. Gradually stir in the powdered sugar until combined. Stir in the vanilla and caramel until combined. Pour evenly over the warm cake. Let set for about 15 minute before slicing and serving.