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 over a pan of simmering water, stirring constantly, until it begins to thicken (10 - 15 minutes). Remove from the heat and allow to cool a little.

Pour the cream into a bowl and whisk until it stands in soft peaks, then fold it into the chocolate mixture.

If you have an ice cream machine use it from here. If not, transfer the ice cream to a suitable container and leave in the freezer for 1 hour. Remove, beat the ice cream until smooth and return it to the freezer. Repeat until the ice cream has small crystals and can retain a good shape.