Preheat oven to 350°F (175°C). Line a 9x9-inch pan with parchment paper, leaving an overhang.

In a large bowl, whisk melted butter and sugar. Add eggs and vanilla, whisking well until glossy.

In a separate bowl, whisk flour, cocoa powder, baking powder, and salt. Add dry ingredients to the wet, folding with a spatula until just combined. Do not overmix.

Pour batter into the prepared pan and bake for 22-25 minutes. A toothpick should have moist crumbs.

Let the brownie cool completely in the pan.

For the soak: Mix cooled coffee, sugar, and liqueur. Poke the cooled brownie all over with a fork and pour the soak evenly on top. Let sit 15 minutes.

For the topping: In a large, chilled bowl, beat the cold mascarpone, cold heavy cream, powdered sugar, and vanilla with an electric mixer until thick, stiff peaks form (3-5 minutes).

Spread the mascarpone topping evenly over the coffee-soaked brownie.

Cover and refrigerate for at least 4 hours, or overnight, to set.

Before serving, lift the slab out using the parchment paper. Dust generously with cocoa powder and slice into squares.