Preheat the oven to 350 degrees F. Spray an 8x8-inch pan with nonstick baking spray.
In a bowl of an electric stand mixer fitted with a paddle attachment, cream together the butter and brown sugar for 2 minutes.
Mix in the egg and sour cream.
In a separate bowl, whisk together the molasses and hot water until mixed together completely. Set aside.
In another bowl, whisk together the all-purpose flour, baking soda, baking powder, ground ginger, cinnamon, and ground cloves. Set aside.
Alternate mixing half of the molasses into the batter, with half of the dry ingredients until all is incorporated together. Do not overmix the batter.
Pour batter into the prepared 8x8 pan.
Bake in the oven for 30-35 minutes or until a toothpick inserted into the center of the cake comes out clean. Remove the cake and let it cool while you make the frosting.