Heat the oven to 350. Line 12 muffin cups with paper liners.
In a large bowl, combine the flour, brown sugar, baking soda, ginger, cinnamon, allspice, and salt. Whisk to blend dry ingredients thoroughly.
In a saucepan, combine the water, molasses, and 1/2 cup of butter. Cook over medium heat, stirring constantly, until butter is melted and the mixture just begins to simmer. Remove from the heat.
Whisk the hot mixture into the dry ingredients until blended. Whisk in the lightly beaten egg until the batter is smooth and well blended.
Fill the 12 lined muffin cups about two-thirds full, distributing the batter evenly.
Bake for about 20 minutes, until cupcakes are firm and a toothpick comes out clean when inserted into the center of a cupcake.
Cool in the pan for 5 minutes, then remove the cupcakes to a rack to cool completely.
Makes 12 cupcakes.
Frosting:
Beat the cream cheese with 2 tablespoons of butter until light and creamy. Beat in lemon zest, lemon juice, and the lemon extract and 1/4 teaspoon of vanilla extract.
Slowly beat in 1 1/2 cups of confectioners' sugar. Increase mixer speed and beat for 2 to 3 minutes, adding more confectioners' sugar if a stiffer frosting is desired.
Makes about 1 1/2 to 2 cups of frosting, enough to frost 12 cupcakes or a 1-layer cake.
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