Break the chocolate into small pieces and place in a saucepan with the milk and Kahlua. Set over a low heat and stir until the chocolate has melted. Remove from the heat.
Place the egg and egg yolks with the sugar and cornflour in a heatproof bowl and beat until creamy and fluffy using an electric whisk. Pour in the melted chocolate and whisk well. Make a bain-marie and heat the mixture