Preheat the oven to 350 degrees F. and position the baking rack to the lower position of the oven. Line an 8x8-inch square baking pan with parchment paper. Set aside.
Using a stand mixer with paddle attachment or hand electric mixer, add the 8 tablespoons butter and mix on medium speed until smooth. Add ½ cup granulated sugar and continue mixing until fluffy. Add 1 cup molasses and 1 large egg, continue mixing.
In a separate small bowl, whisk together 2 ½ cups all-purpose flour, 1 ½ teaspoons baking soda, ½ teaspoon salt, 1 tablespoon ground ginger, 1 ½ teaspoons ground cinnamon, ½ teaspoon ground cloves, ½ teaspoon ground nutmeg, and ½ teaspoon allspice until combined.
Turn the mixer on low and gradually add in the flour mixture until it comes together.
Turn the mixer off and slowly pour in the 1 cup hot water and ¼ cup chopped candied ginger. Adjust the mixer to low and mix until everything is combined. Be careful not to overmix.
Pour the gingerbread cake mixture into the prepared baking pan. Place into the oven to bake for about 35 to 40 minutes, until a cake tester comes out with just a few moist crumbs and no wetness.
Carefully remove the cake from the oven. Allow it to cool still in the baking pan on a wire rack for 10 to 15 minutes before removing it from the pan and allowing it to continue cooling completely.
While the cake is cooling on the rack, go ahead and make the cream cheese frosting. Place 8 ounces cream cheese in the stand mixer with a paddle attachment or a large bowl with a hand mixer. Mix the cream cheese for about 1 minute, until it's smooth.
Add the ½ cup butter and continue beating on medium speed for 1 minute, until thoroughly combined.
Turn the mixer on low and add the 2 cups powdered sugar, 2 teaspoons vanilla extract, and ⅛ teaspoon salt. Continue mixing until the frosting is creamy and smooth.
Evenly spread the frosting all over the top of the cooled cake. Use as much or as little of the frosting as you prefer. Sprinkle the top with more chopped candied ginger and pomegranate arils. Cut the cake into squares and serve. Enjoy!