Prepare the Oven: Preheat the oven to 350°F (175°C). Grease an 8x8-inch baking pan and line it with parchment paper for easier removal.
Combine Wet Ingredients: In a mixing bowl, whisk together the melted butter, brown sugar, and molasses until the mixture is smooth. Add the eggs and vanilla extract, whisking until fully incorporated.
Mix Dry Ingredients: In a separate bowl, sift together the flour, baking powder, ground ginger, cinnamon, nutmeg, and salt.
Create the Batter: Gradually mix the dry ingredients into the wet ingredients. Stir until just combined, ensuring not to overmix.
Bake: Pour the batter into the prepared pan, smoothing it out evenly. Bake for 25-30 minutes, or until a toothpick inserted into the center comes out with moist crumbs. Allow the brownies to cool completely in the pan.
Make the Frosting: In a separate bowl, beat the softened cream cheese and butter until creamy. Gradually add the powdered sugar, followed by the eggnog and vanilla extract. Beat until smooth and spreadable.
Assemble the Brownies: Spread the eggnog frosting evenly over the cooled brownies. Garnish with a light sprinkle of ground nutmeg for a festive touch.