In a 2- to 3-quart pan over high heat, bring 1 cup water to a boil. Remove from heat and stir in molasses and baking soda. After mixture stops foaming, stir in 1/2 cup cold water; let cool to room temperature, stirring often, about 10 minutes.
In a small bowl, whisk together flour, baking powder, cinnamon, ginger, salt, and cloves.
In a large bowl, with an electric mixer on high speed, beat butter and brown sugar until well blended. Beat in eggs until blended. Reduce speed to medium-low. Add flour and molasses mixtures alternately until incorporated, then beat on high speed until well blended. Pour into a buttered and floured 9-inch square pan.
Bake in a 325° regular or convection oven until a toothpick inserted in center of thickest part comes out clean, 45 to 50 minutes. Let cool in pan on a rack at least 1 1/4 hours.