Into a bowl sift together the flour, the ground ginger, the cinnamon, the cloves, the allspice, and the salt. In another bowl cream 1/2 stick of the butter, add the granulated sugar, and beat the mixture until it is fluffy.
Beat in the molasses and the egg, beating until the mixture is smooth. In a measuring cup combine the baking soda with 1/2 cup boiling water and stir the mixture to dissolve the baking soda.
Stir the mixture into the molasses mixture (the mixture will appear curdled) and stir the molasses mixture into the flour mixture, stirring to combine the ingredients well.
Line twelve 1/2-cup muffin tins with paper liners and spoon the batter into the liners, filling them halfway. Bake the cupcakes in the middle of a preheated 350°F oven for 20 minutes, or until a tester comes out clean. (The cupcakes will be flat or slightly indented on top.)
Transfer the cupcakes to a rack and let them cool.
In a bowl cream together the cream cheese, and the remaining 2 tablespoons butter, add the confectioners' sugar and the vanilla, and beat the mixture until it is fluffy and smooth.
Beat in the zest and the lemon juice and chill the frosting for 30 minutes. Spread the frosting on the cupcakes and top each cupcake with some of the crystallized ginger.