Preheat oven to 350°. In a bowl, cream butter and sugar until light and fluffy, 5-7 minutes. Beat in eggs and vanilla. Stir in applesauce. Combine flour, baking soda and spices; stir into creamed mixture. If desired, fold in nuts.
Fill greased or paper-lined muffin cups three-fourths full. Bake until a toothpick comes out clean, 20-25 minutes. Cool 5 minutes before removing from pans to wire racks. If desired, sprinkle with cinnamon sugar.