Preheat your oven to 350°F (175°C). Grease two 8-inch round cake pans with butter or non-stick spray and line the bottoms with parchment paper to ensure the cakes release easily after baking.
In a medium-sized mixing bowl, whisk together the flour, ground ginger, cinnamon, cloves, nutmeg, baking soda, and salt. Make sure all the spices are evenly distributed throughout the flour.
In a large bowl using a hand mixer or a stand mixer, beat the 3/4 cup of softened butter and brown sugar together on medium-high speed until the mixture is light and fluffy, which usually takes about 2-3 minutes.
Add the egg and molasses to the creamed butter mixture. Beat well until fully combined, scraping down the sides of the bowl as needed to ensure everything is incorporated.
Gradually add the dry ingredients to the wet mixture, alternating with the hot water. Start and end with the dry ingredients. Mix until just combined; do not overmix. Pour the batter evenly into the prepared pans and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean. Let the cakes cool completely on a wire rack.
To make the frosting, beat the cream cheese and 1/2 cup of butter until smooth. Add the powdered sugar and vanilla, beating until fluffy. Place one cake layer on a plate, spread a layer of frosting on top, place the second layer over it, and cover the top and sides with the remaining frosting.