6 tablespoons unsalted butter, plus more for pan
6 ounces coarsely chopped good-quality semisweet chocolate
1/4 cup unsweetened cocoa powder (not Dutch-process)
3/4 cup all-purpose flour
1/4 teaspoon baking powder
1/4 teaspoon salt
1 cup sugar
2 large eggs
2 teaspoons pure vanilla extract
Preheat oven to 350 degrees. Line a buttered 8-inch square baking pan with foil or parchment paper, allowing 2 inches to hang over sides. Butter lining (excluding overhang); set pan aside.
Put butter, chocolate, and cocoa in a heatproof medium bowl set over a pan of simmering water; stir until butter and chocolate are melted. Let cool slightly.
Whisk together flour, baking powder, and salt in a separate bowl; set aside.
Put sugar, eggs, and vanilla in the bowl of an electric mixer fitted with the whisk attachment, and beat on medium speed until pale, about 4 minutes.
Add chocolate mixture; beat until combined. Add flour mixture; beat, scraping down sides of bowl, until well incorporated.
Pour batter into prepared pan; smooth top with a rubber spatula. Bake until a cake tester inserted into brownies (avoid center and edges) comes out with a few crumbs but is not wet, about 35 minutes. Let cool slightly in pan, about 15 minutes. Lift out brownies; let cool completely on a wire rack before cutting into squares