How to make your own Carrot Cake

Here is my recipe for making a carrot cake from scratch.  So far, so good. My kids and husband don't like nuts, so I didn't make this recipe with nuts, but you can add them if you like.  I also didn't add pineapple because the kids won't eat anything that may be slimy in the cake, so you can add a can of crushed pineapple that has been well drained if you like.

Ingredients:
4 eggs
3/4 cups vegetable oil
1/2 cup applesauce
2 cups brown sugar
1 Tablespoon vanilla extract (the real one, not artificial)
2 cups all-purpose flour
2 teaspoons baking soda
2 teaspoons baking powder
1/2 teaspoon salt
1Tablespoon ground cinnamon
1 teaspoon nutmeg
4 cups grated carrots

Icing:
1/2 cup butter, softened
8 ounces cream cheese, softened (I use the lower fat one, but it doesn't taste as good)
4 cups confectioners' sugar
1 teaspoon vanilla extract

Directions:
Preheat oven to 350 degrees F (175 degrees C). Grease and flour a 9x13 inch pan.
In a large bowl, beat together eggs, oil, applesauce, brown  sugar and vanilla. In separate bowl, mix flour, baking soda, baking powder, salt, nutmeg and cinnamon. Add to wet mixture and stir just until all flour is moistened (if you stir too much, it will be dense). Stir in carrots - just until mixed  in. Pour into prepared pan.
Bake in the preheated oven for 40 to 50 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.

Icing:
In a medium bowl, combine butter, cream cheese, confectioners' sugar and 1 teaspoon vanilla. Beat until the mixture is smooth and creamy. Frost the cooled cake. --- Just a small fyi: It's much easier to do if the cream cheese and butter have sat out until they reach room temp.  It's almost impossible if the butter is cold, and just harder if the cream cheese is cold.