Preheat oven to 350°F (175°C) and butter an 8-inch square pan, lining it with parchment. Melt the butter and chocolate together in a heatproof bowl over simmering water until smooth, about 3 minutes. Let cool slightly.

Whisk both sugars into the warm chocolate mixture. Add eggs one at a time, whisking well after each, then stir in vanilla.

Sift the flour, cocoa powder, baking powder, and salt directly over the bowl. Add espresso powder if using. Fold gently with a spatula until no flour streaks remain.

Scrape batter into the pan and smooth the top. Bake 30 to 35 minutes, until a toothpick inserted in the center comes out with moist crumbs. Cool completely in the pan on a wire rack.

Lift out using the parchment, slice into squares, and serve.