Prepare 10 paper cupcake liners by brushing their interiors with a little butter.

Dust the buttered liners with unsweetened cocoa powder, then place them in the 10-cup muffin tin.

Chop 400 g dark chocolate into small pieces and place it in a heatproof bowl with 250 g butter.

Set the heatproof bowl over a saucepan of gently simmering water and melt the chocolate and butter.

Whisk 6 eggs with 130 g granulated sugar in a mixing bowl until smooth and homogeneous.

Whisk 100 g all-purpose flour and 5 ml vanilla extract into the egg mixture until no flour streaks remain.

Pour the melted chocolate-butter mixture into the egg mixture and fold until the batter is glossy and uniform.

Divide the batter among the 10 prepared liners, filling each liner about three-quarters full.

Freeze the filled cakes until completely firm, at least 2 hours.

Preheat the convection oven to 190°C (375°F) and bake the cakes directly from frozen for 9 to 10 minutes.

Rest the cakes for 1 minute, then dust them with icing sugar and serve immediately while the centers are molten.