Heat oven to 375 F. Line a muffin tin with paper liners.
In a large bowl, combine sugar, butter, water, molasses, and eggs.
Stir in baking soda, salt, ginger, cinnamon, and allspice. Gradually add flour a little at a time until just combined.
Fill cupcake liners ~2/3 of the way full.
Bake for 16-18 minutes or until a toothpick inserted in the center comes out clean.
Allow cupcakes to sit in pan for 3-4 minutes. Move to a wire rack to cool completely before frosting.
<b> For the Brown Sugar Cream Cheese Frosting </b>
Beat butter and cream cheese until light and fluffy.
Stir in vanilla, and brown sugar. Mix until brown sugar is dissolved.
Spread or pipe frosting onto gingerbread cupcakes. Refrigerate for 30-60 minutes or until frosting is set.
Garnish with a gingerbread cookie, if desired.