Preheat the oven to 200°C (390°F). Generously grease four ramekins with butter and set aside.
Chop the dark chocolate into small pieces and melt it together with the butter using a double boiler or microwave in short bursts, stirring until smooth and glossy. Smell that rich cocoa aroma filling the air.
In a separate bowl, whisk the eggs, sugar, and vanilla extract until the mixture is slightly frothy and pale, about 1-2 minutes.
Gently fold the cooled chocolate mixture into the egg mixture using a spatula, combining until smooth.
Sift the flour and cocoa powder into the batter, then carefully fold them in just until combined, avoiding overmixing to keep the batter airy.
Divide the batter evenly among the prepared ramekins, filling each about three-quarters full. Gently tap the ramekins on the counter to release any air bubbles.
Bake in the preheated oven for 12-14 minutes until the edges are set but the center still jiggles slightly when gently shaken. The surface may crack, hinting at the molten core inside.
Remove the ramekins from the oven and let sit for 2 minutes. Carefully run a knife around the edges to loosen, then invert onto serving plates.
Gently lift the ramekins away, revealing the cracked top and the luscious, molten chocolate inside that flows out when cut.
Serve immediately while warm, enjoying the contrast between the tender crust and the silky, velvety, molten center.
