Begin by setting out the butter and cream cheese for the frosting to come to room temperature.
Preheat oven to 350 degrees.
In a stand mixer, combine the brown sugar, sugar, coconut oil, eggs, applesauce, vanilla, and carrots.
Mix thoroughly until all the ingredients are combined.
Add in dry ingredients: flour, baking powder, baking soda, salt, cinnamon, ginger, and nutmeg.
Turn mixer back on and mix again until all ingredients are combined.
Lightly grease two 9 inch spring form pans.
Pour batter into the pans, half in each.
Bake for 28-30 minutes, or until toothpick inserted in to middle comes out clean.
Cool cakes on cooling rack for at least 30 minutes before removing the springform.
Allow cakes to completely cool before frosting. This will take at least 1 hour.