1. Preheat your oven to 350°F and prepare a 9-inch square baking pan by greasing and flouring it.
2. In a large bowl, beat the sugar and butter together until the mixture is pale and fluffy.
3. Beat in the egg, followed by the applesauce and molasses, mixing until well combined.
4. In a separate bowl, sift together the flour, baking soda, salt, cinnamon, ginger, and cloves.
5. Gradually add the dry ingredients to the wet mixture, blending thoroughly.
6. Stir in the hot water until the batter is smooth.
7. Pour the batter into the prepared pan and bake for about 45 minutes, or until a toothpick inserted in the center comes out clean.
8. Allow the cake to cool completely in the pan.

To Make the Frosting:

1. In a medium bowl, combine the cream cheese and butter and beat until the mixture is smooth and creamy.
2. Add vanilla and cinnamon, mixing well.
3. Slowly add the powdered sugar, beating until the frosting is fluffy.
4. Blend in the molasses until evenly incorporated.
5. Once the cake is fully cooled, spread the frosting over the top and finish with a light dusting of cinnamon.