Preheat oven to 350°F. Mix flour, ginger, baking powder, cinnamon and salt in medium bowl. Set aside.
Beat butter, molasses and brown sugar in large bowl with electric mixer on medium speed until well blended and smooth. Add egg and applesauce; mix well. Add flour mixture alternately with milk, beating on low speed after each addition.
Spoon batter into 15 paper-lined muffin cups, filling each cup 3/4 full. Sprinkle with granulated sugar.
Bake 15 to 20 minutes or until toothpick inserted into muffin comes out clean. Serve warm.