Preheat oven to 350°F (175°C). Grease a donut pan.
In a bowl, mix flour, baking powder, baking soda, cinnamon, ginger, allspice, cloves, and salt.
In another bowl, whisk brown sugar, egg, molasses, milk, vanilla, and melted butter.
Combine wet and dry ingredients until smooth.
Fill donut pan cavities ⅔ full.
Bake for 10-12 minutes until a toothpick comes out clean.
Cool donuts on a wire rack.
Mix confectioner's sugar, hot water, eggnog, and maple syrup for icing.
Dip cooled donuts in icing and sprinkle with gingersnap crumbs.