Preheat the oven to 350 degrees. Line 14 to 15 muffin cups with paper liners and set pans aside.

Bring the 1/2 cup lukewarm water to a boil in a small saucepan. Remove from the heat and stir in the molasses and baking soda. The mixture will start to foam after a bit; when it stops foaming, add the cold water. Cool mixture to room temperature.

Combine the butter and brown sugar in a large mixing bowl and beat with an electric mixer on medium speed until very creamy. Add the egg and beat to combine. Beat in the baking powder, spices, and salt.

Turn mixer to medium speed and add the flour mixture in three additions, alternating with the cooled molasses mixture, beginning and ending with the flour. Beat until flour is just incorporated.

Fill prepared muffin cups 2/3 full and bake cupcakes 14 to 18 minutes, until a toothpick inserted into the center of the cupcakes comes out clean. Set pans on a wire rack and cool cupcakes for 10 minutes, then remove cupcakes from the pans to the racks to cool completely before frosting.

Beat the butter and cream cheese in a medium mixing bowl with an electric mixer very light and creamy. With mixer on low, gradually add 2 1/2 cups of powdered sugar, mixing until combined. Beat in the vanilla and salt.

Scrape down the sides and bottom of the bowl, then turn mixer to medium and beat until smooth. Add more powdered sugar if necessary to achieve desired consistency.

Frost cupcakes as desired and serve. Uneaten cupcakes can be stored, loosely covered with plastic wrap, in the fridge for up to 2 days, or in the freezer in airtight containers for up to 2 months.