In a bowl, and with an electric mixer, cream together the applesauce, oil, water, sour cream and eggs until smooth. Add the brown sugar, white sugar, vanilla and spices. Once smooth, add the flour and mix. Once the batter is combined, fold in the chopped apples and combine. Spray and flour a bundt pan. Bake at 350 for 55 minutes or until center is no longer soft. You will want to cook it a little longer than you think because it is super thick and very moist.
FROSTING:
In a bowl and with an electric mixer, beat the butter until creamy and smooth. Add the rest of the ingredients until smooth. Add enough powdered sugar to create a frosting the consistency you would like. You can make a thin glaze, or a thick glaze that can be frosted once the cake is cooled and will be more thick. Either way is delicious!
If you are using a more thin glaze, drizzle half of the frosting on the hot cake. When it has cooled for a few minutes and is no longer piping hot, drizzle the rest of the frosting over the cake. Pour down the tops of the cake and let it drizzle down the sides of the bundt.