In a large bowl, beat together eggs, oil, white and
brown sugar and 2 teaspoons vanilla. Mix in flour,
baking soda, baking powder, salt, nutmeg and
cinnamon. Stir in carrots, apple sauce, and
pineapple. Pour into prepared pan.
To Make Frosting- 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.