Combine brown sugar with grated carrots, mix together & let sit 1 hr
Preheat oven to 350 degrees
Grease 2 - 10 inch cake pans
In a large bowl, beat eggs until light, gradually beat in white sugar, oil & vanilla
Stir in applesauce
Combine flour, baking soda, baking powder, salt, cinnamon, nutmeg, cloves & ginger in separate bowl & stir into wet mixture until absorbed
Stir in the carrot mixture that's been sitting & walnuts
Pour evenly into pans the 10 inch pans
Cook 30-35 mins or until toothpick tests clean