Preheat your oven to 425F. Generously grease four 6-oz ramekins with butter, then dust the insides with cocoa powder, tapping out the excess. Place the ramekins on a baking sheet.
Melt the semi-sweet chocolate and butter together in a microwave-safe bowl in 30-second intervals, stirring between each, until completely smooth. Let cool for 2 minutes.
Whisk the powdered sugar into the melted chocolate mixture until well combined and smooth.
Add the eggs, egg yolks, and vanilla extract. Whisk vigorously until the batter is thick, glossy, and well combined.
Add the flour and salt. Gently fold with a spatula until just combined and no streaks of flour remain. Be careful not to overmix.
Divide the batter evenly among the prepared ramekins, filling each about three-quarters full. Bake for 12-14 minutes until the edges are firm and set but the center is still soft and jiggly when you gently tap the ramekin.
Let the cakes rest for exactly 1 minute. Run a thin spatula gently around the edges of each ramekin, then invert onto serving plates. Wait 10 seconds and carefully lift the ramekin away. Dust with powdered sugar and serve immediately while the center is still molten.