Prepare a 9x13" pan by lightly greasing. Preheat oven to 350F.
Beat together in a bowl of a standup mixer with a paddle attachment the applesauce, oil, sugar, eggs and vanilla. Whisk together the flour, baking soda, baking powder, salt, cinnamon and nutmeg. Add slowly to the applesauce mixture. Fold in the carrots, coconut, walnuts and pineapple.
Pour into the prepared pan. Bake for 35-40 min. or until a toothpick comes out clean. Let cool completely.
For the frosting: In the a standup mixer with a paddle attachment beat the butter with the cream cheese until fluffy. Add in the vanilla and icing sugar slowly. Beat until smooth. Ice the cooled cake and refrigerate until cooled and set.
Nutrition calculation is an estimation only. If you need nutritional calculations for medical reasons, please use a source that you trust.