Heat oven to 400F. Grease cookie sheets. Cream the sugars and butter together until smooth and creamy. Add eggs, vanilla and applesauce. Mix together the dry ingredients and add to creamed mixture. If raisins or nuts are desired, add now, then spoon 2 heaping tablespoons per cookie onto cookie sheet. Bake about 8 minutes, until light, golden brown. Remember they will continue to bake for a little white after they come out of the oven. Dust with powdered sugar.
You can also bake these as bars by spreading the mixture out in a well-greased, or foil-lined baking pan for about a half an hour in a 350F oven. Dust with powdered sugar and cut into squares.