Melt the chocolate and butter together in a heatproof bowl set over barely simmering water, or microwave in 20-second bursts, stirring until smooth.
In a stand mixer fitted with the whisk, beat the eggs and both sugars on high until pale and airy, about 5 minutes.
Fold the melted chocolate into the whipped eggs until just combined and streaks disappear.
Sift in the cornstarch, cocoa, baking powder, and salt; fold gently until a thick, glossy batter forms.
Portion the batter into 16 rounded mounds (about 45 grams each) on a parchment-lined baking sheet, spacing them 2 inches/5 cm apart; shape lightly into rounds.
Sprinkle with flaky sea salt and bake in a preheated 355°F/180°C oven for 10 minutes, until the tops crack but centers remain soft. Cool on the sheet for 10 minutes, then transfer to a wire rack to finish cooling.