Preheat the oven to 325°F. Spray a 9x9-inch baking dish with nonstick cooking spray. Set aside.
In the bowl of a stand mixer with a paddle attachment, cream butter and sugar until light and fluffy.
Add the molasses and egg. Beat until smooth.
In a large bowl, whisk together the flour, baking soda, ginger, cinnamon, and salt.
Add about 1/3 of the dry ingredients to the butter and sugar mixture, mixing until just combined (don't overmix). Add half the water, followed by another third of the dry ingredients. Pour in the remaining water and add the final third of the dry ingredients. Mix until combined.
Pour batter into prepared baking dish. Bake 45-50 minutes. (Check the cake after about 30 minutes; cover with aluminum foil if the edges are getting too dark.) The cake is done when an inserted toothpick comes out with a few crumbs, but no wet batter. Remove from the oven and let cool as you prepare the pudding.