- STEP 1
1. Preheat the oven to 350 degrees F. Spray a 9- by 13-inch baking dish with nonstick cooking spray.
- STEP 2
2. Using a hand or stand mixer, mix the eggs, oil, applesauce, and vanilla extract on low speed for 30 seconds. Beat in both sugars on medium speed until well combined, 2 minutes. Add the flour, baking powder, cinnamon, salt, and nutmeg. Mix the batter until the dry ingredients are fully incorporated. Stir in the carrots on low speed until they are evenly distributed within the batter. Pour the batter into the baking dish and spread it evenly with a spatula.
- STEP 3
3. Bake for 40 to 45 minutes, until the center of the cake springs back when touched. Allow the cake to cool completely in its pan before topping it with the Whipped Cream Cheese Frosting. If you like, sprinkle the frosted cake with toasted coconut. Cut into squares to serve.
- STEP 4
4. To make the frosting: Using a hand or stand mixer, whip all the ingredients together on low speed until the sugar is fully absorbed. Increase the speed to medium-high and blend until the mixture resembles frosting. Don't worry if the mixture initially looks curdled. Keep whipping it and watch it transform into a thick frosting.