Preheat the oven to 350°F (175°C). Lightly grease a 9-inch (23 cm) square metal baking pan. Line it with parchment paper, leaving an overhang on two sides to help lift out the brownies.

Place the butter and chopped semisweet chocolate in a medium heatproof bowl. Microwave in 20-second intervals, stirring after each interval, until almost completely melted. Stir until smooth and glossy. Let the mixture cool for about 5 minutes so it is warm rather than hot.

Stir the espresso powder and hot water together in a small bowl until no dry granules remain. Set aside briefly.

In a large mixing bowl, whisk the granulated sugar, brown sugar, and eggs for 1 to 2 minutes. The mixture should look smooth, slightly thickened, and lighter in color.

Whisk the melted chocolate mixture, dissolved espresso, and vanilla into the eggs. Continue whisking until the batter is uniformly dark and glossy.

In a separate bowl, whisk together the flour, cocoa powder, and salt. Break up any visible lumps of cocoa powder.

Add the dry ingredients to the chocolate mixture: Fold gently with a flexible spatula just until no streaks of flour remain. The batter should be thick, glossy, and slowly spread when pushed with the spatula. Do not continue mixing once the dry ingredients are incorporated.

Scrape the batter into the prepared pan and spread it evenly into the corners. Smooth the top with the spatula so the brownie layer bakes at an even thickness.

Bake on the center rack for 30 to 35 minutes. The edges should look set and slightly raised, while the center should no longer appear wet. A toothpick inserted about 1 inch from the edge should come out with moist crumbs but no liquid batter.

Place the pan on a wire rack and let the brownies cool for 30 minutes. Use the parchment overhang to lift them from the pan, then place them on the rack and cool for another 1 hour. The surface must feel completely cool before the topping is added.

Place the cold mascarpone, powdered sugar, and vanilla in a large mixing bowl. Beat on low speed for about 20 seconds, just until combined and smooth. Avoid prolonged mixing because mascarpone can become grainy if overworked.

With the mixer running on low, gradually pour in the cold heavy cream. Increase to medium speed and whip for 1 to 3 minutes, until the mixture forms medium peaks. The cream should hold its shape when the beaters are lifted but still look smooth and spreadable. Stop immediately if it begins to look stiff or grainy.

Spread the mascarpone cream evenly over the completely cooled brownie slab with an offset spatula. Create a smooth surface or shallow swirls without pressing heavily into the brownies.

Place the remaining cocoa powder in a fine-mesh sieve and dust it evenly over the chilled mascarpone layer. Apply the cocoa shortly before serving for the driest, most defined finish.

Cut the brownies into 16 squares with a sharp knife. Wipe the blade clean between cuts to keep the mascarpone layers neat. Serve chilled or let the brownies stand at room temperature for about 10 minutes for a softer texture.