Preheat the oven to 425°F (220°C).
Generously butter two 6-ounce ramekins and lightly dust them with cocoa powder. Tap out any excess.
Place the chopped chocolate and butter in a microwave-safe bowl.
Microwave in 20-second intervals, stirring between each interval, until completely melted and smooth.
In a separate bowl, whisk together the egg, egg yolk, sugar, and vanilla extract until slightly thickened and pale.
Slowly pour the melted chocolate mixture into the egg mixture while whisking continuously.
Add the flour and salt and gently fold until fully combined.
Divide the batter evenly between the prepared ramekins.
Place the ramekins on a baking sheet.
Bake for 10 to 12 minutes, or until the edges are set but the centers still look slightly soft.
Remove from the oven and let stand for 1 minute.
Carefully run a knife around the edges and invert each cake onto a serving plate.
Dust with powdered sugar and serve immediately.