Preheat your oven to 350 degrees Fahrenheit. Grease and line a 9x13-inch metal pan with parchment paper. You can use metal binder clips to secure the parchment paper on the sides.
In a medium-sized bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, ginger, nutmeg, and cloves. Set aside.
In a large bowl, whisk together the oil, brown sugar, applesauce, eggs, and vanilla extract until well combined.
Gradually fold the dry ingredients into the wet ingredients using a rubber spatula until no streaks of flour remain. Do not overmix.
Spread the batter evenly into the prepared pan. Bake for 45-50 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely. Mine took the whole time, but my oven runs cooler.
For the cream cheese frosting
In the bowl of an electric mixer, with the paddle attachment combine the room temperature butter and cream cheese. Beat on medium speed for about 2 minutes until creamy.
Scrape down the sides and bottom of the bowl, then beat for an additional 2 minutes.
With the mixer on low, gradually add the sifted powdered sugar, followed by the heavy whipping cream, vanilla extract, and a pinch of salt.
Increase the mixer speed to medium-high and beat for 3 to 5 minutes until the frosting is smooth and fluffy.
To ensure a consistent texture, manually eliminate air pockets by gently folding the frosting with a rubber spatula or wooden spoon.
Once the cake is fully cooled, use an offset spatula to frost the top with the cream cheese frosting. This cake can be served at room temperature or chilled, based on preference.