Preheat your oven to 350°F (175°C) and grease a 9x13-inch baking pan.

In a large mixing bowl, combine the melted butter and granulated sugar. Mix until well combined.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In a separate bowl, whisk together the flour, cocoa powder, baking powder, and salt. Gradually add the dry ingredients to the wet mixture, stirring until just combined.

Pour the brownie batter into the prepared baking pan and spread it evenly. Bake for 25-30 minutes or until a toothpick inserted in the center comes out with a few moist crumbs.

While the brownies are baking, mix the cooled coffee and coffee liqueur (if using) in a shallow dish.

Once the brownies are done baking, let them cool in the pan for about 10 minutes. Then, carefully remove them from the pan and place them on a wire rack to cool completely.

When the brownies are cool, use a skewer or toothpick to poke holes all over the top. Brush the coffee mixture over the brownies, allowing it to soak in.

In a mixing bowl, beat the mascarpone cheese, heavy cream, and powdered sugar until smooth and creamy. Spread this mixture over the brownies.

Dust the top with cocoa powder before slicing into squares and serving.