Preheat oven to 350 and line round pans with parchment paper. Grease the pans.
Mix together the flour, baking powder, baking soda, cinnamon, nutmeg, ginger, cloves, and salt in a bowl and set aside.
In another bowl mix the carrots, applesauce, vanilla, oil, sugars and egg YOLKS. Set aside.
Whip the egg WHITES with a stand mixer or handheld mixer until you get stiff peaks.
Carefully add the dry ingredients to the wet, in increments and mix until blended. Fold in the egg whites just enough so there is no more egg white visible. Fold in any other ingredients that you would like in your cake (raisins, coconut, pecans, etc.)
Divide the batter into the two cake pans and bake for 35 mins or until a fork comes out clean. While the cakes are baking, prepare the icing.
Once the cakes have COOLED COMPLETELY. You can start frosting them and garnish as you please!