Preheat your oven to 375°F. Spray a 10x15-inch jelly roll pan with non-stick cooking spray, making sure it’s well-coated to prevent the cake from sticking.
In a large bowl, whisk together the flour, sugar, baking soda, cinnamon, and salt. This will ensure that all the dry ingredients are evenly distributed in the cake batter.
In a medium saucepan, heat the butter and water over medium-high heat. Stir occasionally until the butter melts and the mixture begins to simmer. Once simmering, remove the saucepan from the heat.
Pour the hot butter and water mixture into the bowl with the dry ingredients. Stir until everything is just combined. Be careful not to over-mix.
Add the lightly beaten eggs, sour cream, and vanilla extract to the mixture. Stir until smooth and fully combined. The batter should be thick and creamy.
Pour the batter into the prepared jelly roll pan, spreading it evenly. Bake in the preheated oven for 18-22 minutes, or until a toothpick inserted in the center comes out clean. Let the cake cool in the pan for 5-10 minutes, just until warm.
While the cake cools, make the frosting. In a medium saucepan, melt the butter and milk over medium heat. Once the butter is fully melted, raise the heat to medium-high and bring the mixture to a simmer. Remove from heat and whisk in the powdered sugar, vanilla extract, and cinnamon until smooth and combined.
Pour the frosting over the warm cake and spread it out evenly with a spatula. Let the frosting settle into the cake as it cools.
In a large pot, melt the butter over medium heat. Add the diced apples and cook for about 5 minutes, stirring frequently. In a small bowl, combine the brown sugar, corn starch, and cinnamon. Stir this mixture into the apples and cook until the apples are tender, about 10-12 minutes. Be sure not to overcook them; they should still hold their shape.
Remove the apple topping from the heat and let it cool to room temperature. Once the apples are cool, spread them evenly over the frosted cake. Drizzle with caramel sauce, if desired, and serve. Enjoy this Caramel Apple Sheet Cake with your loved ones, and share the warmth and flavors of Southern comfort.