Preheat your oven to 350 degrees Fahrenheit. Line an 8×8 inch square baking pan with parchment paper, leaving a slight overhang on the sides to make the brownies easy to lift out later. Lightly grease the parchment with a bit of butter or oil to ensure nothing sticks.
In a large mixing bowl, whisk together the melted butter and granulated sugar until well combined. Add the molasses, the egg, and the alcohol-free vanilla extract. Whisk vigorously until the mixture is smooth and the egg is fully incorporated into the batter.
Sift the all-purpose flour, cocoa powder, ground ginger, cinnamon, cloves, and salt directly into the wet ingredients. Using a rubber spatula, gently fold the dry ingredients into the molasses mixture. Be careful not to overmix, stop as soon as you no longer see streaks of white flour.
Spread the batter evenly into the prepared baking pan. Bake for 22 to 25 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached. Do not overbake, as these brownies are best when they are slightly fudgy. Remove from the oven and let them cool completely in the pan.
While the brownies are cooling, prepare the frosting. In a medium bowl, beat the softened cream cheese and softened butter together until smooth and creamy. Gradually add the powdered sugar and the alcohol-free vanilla extract. Beat on medium-high speed until the frosting is light and fluffy.
Once the brownies are entirely cool, use the parchment paper to lift them out of the pan. Spread the cream cheese frosting evenly over the top using an offset spatula. Slice into 16 squares and serve. For the cleanest cuts, wipe your knife with a warm, damp cloth between each slice.
