Position the oven rack lower and warm up your oven to 350°F or 177°C. Grease a 9-inch or 10-inch springform pan. An 11x7-inch rectangle pan or a 9-inch square pan also works fine.
Whisk the all-purpose flour, ground ginger, cloves, cinnamon, baking soda, and salt in a medium bowl. Put it aside.
Take a cup or a separate bowl to mix the molasses in the hot water (about 100°F).
Cream ½ cup of butter in a bowl for 1 to 2 minutes using a handheld or a stand mixer with the paddle attachment. Beat the brown sugar at high speed for 1 minute. Add the vanilla extract and the egg and beat on medium-high until nicely incorporated. Scrape down the bowl’s side.
Alternately beat in the dry ingredients (step 2) and the molasses mixture (step 3) on low speed in three batches, starting and ending with the dry stuff. Keep mixing until combined, but don’t overmix it. Whisk the batter to check if any large lumps remain. If yes, continue beating.
Pour the batter into the greased pan and bake it for 35-37 minutes. Test its doneness by poking a toothpick into the center of the cake. Your cake is ready to serve if it comes out clean or with a few crumbs.
Pop the cake out of the oven and let it rest on the wire rack to cool down completely.
Add 2 tablespoons of butter and cream cheese to a large bowl and mix them with a handheld or stand mixer for 2 to 3 minutes. Throw in the confectioners’ sugar, milk, vanilla extract, and spices (ground ginger, cloves, and cinnamon). Mix them for about 20 seconds at low speed and then crank up to high speed until you have a velvety, creamy frosting. Sprinkle some salt if it’s too sweet.
Spread the frosting on top and sides of the cake (if you have enough). Slice it with a greased sharp knife, and enjoy!