Prepare the Cake
Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch sheet pan, or line it with parchment paper.
In a medium bowl, whisk together the flour, baking powder, baking soda, salt, cinnamon, nutmeg, and cloves.
In a large bowl, combine the granulated sugar, brown sugar, eggs, oil, applesauce, and vanilla extract. Mix until smooth.
Gradually add the dry ingredients to the wet mixture, mixing until just combined.
Fold in the grated carrots gently.
Pour the batter into the prepared pan and spread evenly.
Bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Allow the cake to cool completely in the pan.
Make the Cream Cheese Frosting
In a mixing bowl, beat the cream cheese and butter together until smooth and creamy.
Gradually add the powdered sugar, one cup at a time, mixing well after each addition.
Stir in the vanilla extract until combined.
Assemble the Cake
Spread the cream cheese frosting evenly over the cooled cake.
Optionally, garnish with chopped nuts or a sprinkle of cinnamon.
Slice and serve!