Preheat the oven to 400°F (204°C). Generously apply butter or oil to a 10-by-15-inch jellyroll pan or a 16-3/4 by 12-inch sheet pan to prevent sticking.

In a substantial bowl, thoroughly mix the flour, cinnamon, baking soda, salt, granulated sugar, and brown sugar.

In a medium saucepan over medium-high heat, melt the butter with 1 cup of water. Bring the mixture to a boil and then remove it from the heat. Pour this into the bowl containing the flour mixture. Allow it to cool slightly.

Following the slight cooling, incorporate the buttermilk, eggs, and vanilla extract. Stir gently, ensuring not to overmix. Then, fold in the chopped apples.

Transfer the batter into the prepared pan, ensuring an even spread. Bake for approximately 20 minutes if using a jelly roll pan, or 17 minutes for a 16.75 by 12-inch pan. The cake is ready when a toothpick inserted into it comes out clean. Allow the cake to cool in the pan, placed on a wire rack, for 15 to 20 minutes.

In a large, heat-proof bowl, combine the butter and milk. Heat in the microwave until the butter has fully melted.

Gradually mix in the powdered sugar until the mixture achieves a smooth consistency. Stir in the vanilla extract and caramel sauce. If the glaze appears too thin, additional powdered sugar can be added to reach the desired thickness.

Pour the glaze evenly over the cake while it is still slightly warm. The glaze should be allowed to set for approximately 15 minutes before the cake is sliced and served.