Preheat your oven to 425°F (220°C). Grease four 6-ounce ramekins with butter and dust with flour, tapping out any excess.

In a microwave-safe bowl, combine the chopped bittersweet chocolate and ½ cup of unsalted butter. Microwave in 30-second intervals, stirring after each, until the mixture is smooth and fully melted. Set aside to cool slightly.

In a separate bowl, whisk together the granulated sugar, 2 large eggs, and 2 large egg yolks until the mixture is light and slightly thickened.

Gradually add the melted chocolate mixture to the egg mixture, whisking constantly until well combined.

Sift in the all-purpose flour and add the vanilla extract. Gently fold the mixture until just combined and smooth.

Divide the batter evenly among the prepared ramekins.

Place the ramekins on a baking sheet and bake for 12-14 minutes, or until the edges are set but the centers are still soft. The tops should be puffed and slightly cracked.

Let the cakes cool in the ramekins for 1 minute. Then, run a knife around the edges to loosen and invert each ramekin onto a plate. Serve immediately, ideally with a scoop of vanilla ice cream or a dollop of whipped cream.