Preheat oven to 350℉. Spray a 9 x 13 inch baking pan with non-stick cooking spray.
Beat eggs, vegetable oil, applesauce, sugar, brown sugar, and vanilla together in a large bowl.
Add in flour, baking powder, baking soda, cinnamon, salt, and nutmeg and mix well.
Fold in zucchini and stir until completely mixed in. Pour batter into prepared 9 x 13 inch pan.
Bake for 35-40 minutes or until toothpick inserted into the center comes out clean.
While the cake cools, mix together frosting ingredients and spread over the top of the cooled cake.
If desired, sprinkle the top of the cake with cinnamon and sugar.
Notes
Storage Suggestions: Keep covered at room temperature for up to 2 days and then in the refrigerator for up to 5 days.Freezer Tips: This cake can be frozen for up to 2 months, but I recommend slicing it into individual slices and wrapping each slice in plastic wrap to protect it from freezer burn.Eliminate Extra Liquid: Be sure to pour out any excess liquid from your zucchini after you shred it to make sure to get the right consistency, but there is no need to pat it dry.
Zucchini Prep: We do not peel the zucchini when we shred it but if you prefer it peeled it will still work in the recipe.