Preheat oven to 350°F / 175°C and line 2 baking sheets with parchment paper.
Melt chocolate and butter together in a heatproof bowl (microwave in short bursts, stirring until smooth). Let cool slightly.
In another bowl, whisk eggs, brown sugar, and granulated sugar until thick and glossy (about 2–3 minutes).
Stir melted chocolate mixture and vanilla into the egg mixture until smooth.
In a separate bowl, whisk flour, cocoa, baking powder, and salt. Fold gently into the batter.
Let batter rest 10 minutes to thicken.
Scoop heaping tablespoons onto baking sheets, leaving space. Sprinkle lightly with flaky sea salt.
Bake 9–11 minutes, until edges are set but centers look soft and crackly.
Cool 5 minutes on the tray, then transfer to a rack. Enjoy warm and fudgy!