Preheat the oven to 350F. Spray a 9 x 9 baking dish with nonstick cooking spray and line with parchment paper.
Add the butter to a large mixing bowl and pour the boiling water over it; set aside for a few minutes. Then, whisk until the butter has fully melted.
Add brown sugar, molasses, and egg; whisk until combined.
Slowly add flour, ginger, cinnamon, salt, baking powder, and baking soda; whisk until smooth.
Scoop the batter into a baking dish and bake for 25-35 minutes, or until a toothpick comes out clean. Set aside and allow time to cool.
Using a stand mixer, beat together the frosting ingredients until smooth and fluffy. Add additional tablespoons of heavy whipping cream as needed to reach the desired consistency.
Frost cake or pipe dollops of frosting using a star tip. Slice and serve.