4cupsconfectioners' sugaraka powdered or icing sugar
Preheat oven to 350° F.
Grease and flour a 9x13 inch pan.
In a large bowl, beat together eggs, applesauce, oil, sugars, and 2 teaspoons vanilla.
In a smaller bowl, mix together flour, baking soda, baking powder, salt and cinnamon. Pour flour mixture into egg mixture. Stir in carrots. Pour into prepared pan.
Bake in the preheated oven for 40 to 50 minutes, or until a toothpick inserted into the center¼ of the cake has no uncooked batter on it. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely.
To Make Frosting:
In a medium bowl, combine butter, cream cheese, confectioners' sugar and 1 tsp vanilla. Beat until the mixture is smooth and creamy. Frost the cooled cake.
You can modify the applesauce and oil ingredients, though I recommend using at least 1/2 cup oil to give the cake the best moisture. You can also use all oil (1¼ cups) if you're out of applesauce, but I personally cut it to 1 cup to keep the cake from feeling too heavy.If you like a less sweet, more rich, cream cheese-y, frosting, start with just 2 cups sugar and taste, adding half a cup at a time, up to 4 cups. You'll still get plenty of frosting to cover the cake even if you only use 2 cups sugar.