Preheat oven to 350 degrees
Spray the bottom and sides of 3 9 inch round cake pans
Line with parchment paper that has been cut round to fit inside the cake pans
In a large bowl, mix together the eggs, sugar, and applesauce with a large spoon
Add the flour, baking soda, salt, and cinnamon and stir in completely
Add the carrots, pineapple, coconut, and vanilla; stir/mix in completely
Add the chopped pecans and mix in
Divide evenly among the 3 round cake pans
Bake in the 350 degree oven for 30 minutes
Lower the temperature to 300 degrees and bake for another 30 minutes
Remove from oven and let cool completely in the pans
Once cooled, run a butter knife around the outside of the pans and remove cakes from the pans
Once cooled completely, place 1 layer on a cake plate, frost the top with cream cheese frosting
Place 2nd cake layer on top of the first and frost top
Place 3rd layer on top of the 2nd and frost top and sides of the cake with the cream cheese frosting
Serve