Preheat your oven to 350 degrees Fahrenheit. Grease an 8×8 inch square baking pan with butter or line it with parchment paper, leaving a slight overhang on the sides to make the brownies easier to lift out later.
In a large mixing bowl, whisk together the melted butter, granulated sugar, and brown sugar until smooth. Add the eggs one at a time, beating well after each addition, then stir in the molasses and the alcohol-free vanilla extract until the mixture is glossy.
In a separate medium bowl, whisk together the flour, baking soda, ground ginger, cinnamon, cloves, and salt. Gradually add the dry ingredients to the wet mixture, folding them in gently with a spatula just until no streaks of flour remain. Be careful not to overmix, as this can make the brownies tough.
Spread the batter evenly into the prepared baking pan. Bake for 25 to 30 minutes, or until a toothpick inserted into the center comes out with just a few moist crumbs attached. Remove from the oven and let the brownies cool completely in the pan on a wire rack.
While the brownies cool, beat the softened cream cheese and butter together in a bowl until light and fluffy. Gradually add the powdered sugar and alcohol-free vanilla extract, beating until smooth. Once the brownies are entirely cool, spread the frosting over the top in an even layer. Cut into 16 squares and enjoy.
