Instructions: 1. Preheat your oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan or two 9-inch round cake pans. 2. In a large mixing bowl, sift together flour, baking powder, baking soda, salt, cinnamon, and nutmeg.
3. In another bowl, beat together eggs, sugar, oil, applesauce, and vanilla extract until well combined. 4. Bake for 35 to 40 minutes (for a 9x13-inch pan) or 25 to 30 minutes (for round cake pans), or until a toothpick inserted into the center comes out clean.
5. Allow the cake to cool completely in the pan(s) on a wire rack.
Cream Cheese Frosting: 1. In a large bowl, beat the cream cheese and butter until smooth and creamy. 2. Mix in the vanilla extract. Gradually add the powdered sugar, beating until smooth and creamy.
3. Frost the Cake: Once the cake is completely cooled, frost the top of the cake (if using a single layer) or frost between the layers and on top (if using two layers) with the cream cheese frosting.
4. Serve: Slice and serve the Carrot Cake. Enjoy!