Preheat oven to 350°F / 175°C. Line two baking sheets with parchment paper.
Melt chocolate and butter together in a heatproof bowl (microwave in short bursts, stirring until smooth). Cool slightly.
In another bowl, whisk eggs, brown sugar, and granulated sugar until thick and glossy (about 2–3 minutes).
Stir in melted chocolate mixture and vanilla.
Whisk flour, cocoa, baking powder, and salt together; fold into batter.
Let batter rest 10 minutes.
Scoop heaping tablespoons onto trays. Sprinkle lightly with flaky sea salt.
Bake 9–11 minutes, until edges set but centers look soft and crackled.
Cool 5 minutes on the tray, then transfer to a rack.