Spoon applesauce onto multiple layers of paper towels, spread to an even thickness. Cover with more paper towels and let sit 5 minutes. Scrape into a bowl.
Beat applesauce with 1 cup sugar and butter; beat in molasses and egg.
Mix together flours, baking soda, cinnamon, salt, ginger, and cloves. Slowly add flour mixture into applesauce mixture beating well after each addition. Wrap dough in plastic wrap and freeze for 30 minutes.
Preheat oven to 375 degrees F.
Form dough into 32 (1-inch) balls and roll in 1/4 cup sugar. Arrange dough balls on a cooking spray coated baking sheet and bake 8 to 10 minutes.
Let cool on pans then move to wire racks to continue cooling.