Heat oven to 375 degrees Fahrenheit and line a muffin pan with liners.
Beat together the sugar, butter, molasses, water and eggs on medium speed.
In a separate bowl, whisk together flour, baking soda, salt, ginger, cinnamon and allspice.
Add the dry ingredients to the wet ingredients and mix until well combined.
Spoon about 1/4 cup of the batter into each muffin cup.
Bake 16-18 minutes or until a toothpick inserted into the middle comes out clean. Once done, allow to sit in muffin pan for 5 minutes before moving to cooling racks to finish.
To make the frosting, beat the cream cheese until smooth, scraping down sides as needed.
Add the butter and continue beating until mixture is blended and smooth.
Add the vanilla and brown sugar and beat for 5 minutes until sugar is dissolved and frosting is light and fluffy.
Transfer icing to a piping bag with the star tip and frost tops of each cupcake. Place in the refrigerator for 30 minutes to firm icing.
You can optionally top with a gingerbread man cookie as garnish.