Preheat your oven to 325 degrees Fahrenheit (163 degrees Celsius). Spray a 9×13 metal pan with non-stick spray, line the bottom with parchment paper, and spray again. Use metal binder clips to secure the parchment paper, ensuring they are metal and not plastic. Set aside.
In a medium-sized mixing bowl, whisk together the flour, cinnamon, nutmeg, salt, and baking powder. Set this dry mixture aside.
In a stand mixer fitted with the whisk attachment, combine the granulated sugar, brown sugar, and vegetable oil. Whisk on medium speed for 2 minutes.
Add the eggs to the sugar mixture and continue to mix on medium speed for an additional 2 minutes. Incorporate the vanilla extract and applesauce on low speed just until combined.
Gradually, with the mixer on low speed, add ⅓ of the dry flour mixture. Then add half of the apple cider. Mix until nearly combined, and then add another ⅓ of the dry flour mixture and the remaining apple cider. Finally, add the last ⅓ of the flour mixture and mix until no visible streaks of flour remain.
Evenly distribute the batter into the prepared cake pan. Use the back of a spoon to smooth out the batter for even baking.
Bake for 50-55 minutes. To check for doneness, insert a toothpick into the cake; it's done when it comes out with just a few moist crumbs on it.
Allow the cake to cool completely in the pan. Menwhile, prepare the caramel sauce.
For the Caramel Sauce:
In a medium-sized saucepan, combine water, granulated sugar, and corn syrup. Gently mix together before turning on the heat!
Over medium heat, bring the sugar mixture to a boil. Initially, bubbles will be fast and small, but as it caramelizes, they will slow down and become larger. Do not stir during this process, as it may cause crystallization.
Let the mixture boil until it turns golden brown. This may take a few minutes, so keep a close eye on it to avoid burning.
Heat the cream in the microwave for 1 minute.
Once the caramel achieves a golden brown color, remove it from heat and add the warm cream. Stir until the caramel and cream are thoroughly combined.
Transfer the caramel mixture to a separate bowl, then add vanilla, salt, and butter. Let it sit until the butter melts, and then stir until well incorporated.
For the Cream Cheese Frosting:
In the bowl of an electric mixer, combine the room-temperature butter and cream cheese. Beat on medium speed for about 2 minutes. Scrape down the sides and bottom of the bowl, then beat for an additional 2 minutes.
On low speed, add the sifted powdered sugar, followed by the cream, vanilla extract, and a pinch of salt. Beat on low until fully combined. Scrape down the sides of the bowl.
Increase the mixer speed to medium-high and beat for about 3 to 5 minutes.
Use a rubber spatula or a wooden spoon to remove any air pockets by hand for a smooth consistency.
Assembly:
You can leave the cake in the pan. Once it's completely cool, frost the cake with the cream cheese frosting.
Add dollops of caramel sauce to the frosted cake (you'll only need about half of the caramel; serve the remaining half on the side with each slice).
Swirl the caramel into the cream cheese buttercream.