Preheat oven to 350 degrees.
With an electric mixer, combine eggs, sugar, oil, applesauce, and pumpkin.
In a separate bowl, combine dry ingredients: flour, baking powder, cinnamon, salt, and baking soda.
Add dry ingredients to wet ingredients and combine.
Pour into a greased 9 by 13 inch rectangular baking dish.
Bake at 350 degrees for 30 minutes.
With an electric mixer, combine softened cream cheese, softened butter, confectioner's sugar, and vanilla until smooth and fluffy.
When cake is cooled, frost and cut into bars.
