Chop the dark chocolate into small pieces.

Melt the chopped chocolate in a heatproof bowl set over a pan of simmering water, ensuring the bowl doesn't touch the water.

In a saucepan, combine cream and most of the milk (reserve 1/4 cup) and heat until it is scalding, but not boiling.

Pour half of the hot cream mixture into the melted chocolate and whisk until well combined.

Pour the chocolate mixture back into the saucepan with the remaining cream mixture.

In a separate small bowl, whisk together the reserved milk, cocoa powder, sugar, and cornflour until it forms a smooth paste.

Pour the cocoa paste into the chocolate mixture in the saucepan.

Place the saucepan over low heat and whisk continuously until the mixture comes to a gentle boil and thickens slightly.

Remove from heat and stir in vanilla extract (if using).

Beat briskly with a wire whisk or hand rotary beater until the mixture is foamy.

Pour the hot chocolate into cups and serve immediately.

Top with whipped cream, if desired.