Preheat your oven to 350°F. Line a 9x9-inch baking pan with parchment paper, leaving some extra paper hanging over the sides. This will make it easier to lift the brownies out once they have cooled.In a large mixing bowl, combine the melted butter and brown sugar. Stir until smooth. Add the eggs, molasses, and vanilla extract, then whisk until everything is well combined. In a separate bowl, whisk together the all-purpose flour, ground ginger, cinnamon, baking powder, and salt. Make sure the spices are evenly mixed into the flour.
Slowly add the dry ingredients to the wet mixture. Stir gently until a thick batter forms. Be careful not to overmix. Transfer the batter to your prepared baking pan and spread it evenly with a spatula.
Bake for 28–33 minutes, or until the edges are firm and the center is set. Remove from the oven and let the brownies cool completely in the pan before adding the frosting.
While the brownies cool, beat the softened butter until creamy. Gradually add the powdered sugar, mixing until combined. Add the vanilla extract, cinnamon, and ground ginger.
Add 1 tablespoon of milk or heavy cream and mix. Add a little more if needed to reach your preferred consistency. Beat for another 2–3 minutes until the frosting is smooth and fluffy.
Spread the frosting evenly over the completely cooled brownies. Let the frosting set at room temperature, then refrigerate for 30–60 minutes before slicing into 9 bars.