Preheat oven to 425 degrees Fahrenheit and grease four 6-ounce ramekins with butter and dust with cocoa powder.
Melt the chopped chocolate and butter together in a microwave-safe bowl in 30-second intervals until smooth.
In a separate medium bowl, whisk together the eggs, egg yolks, sugar, and salt until thick and pale yellow.
Whisk the vanilla extract and the melted chocolate mixture into the egg mixture until well combined.
Gently fold in the flour until just incorporated.
Divide the batter evenly among the four prepared ramekins.
Bake for 12 to 14 minutes until the sides are firm but the centers are still soft to the touch.
Let the cakes cool in the ramekins for 1 minute, then run a knife around the edges and invert onto dessert plates.