Put the chocolate pieces and milk in a heavy-based saucepan. Heat gently, stirring, until smooth, then remove from the heat to cool slightly.
Beat the sugar and egg yolks in a bowl until pale and thick. Stir in the cooled chocolate milk, then strain back into the pan. Cook the custard over a gentle heat, stirring all the time, until it thickens and coats the back of a wooden spoon. Don’t allow the mixture boil or it will curdle. Pour into a bowl and leave to cool, stirring occasionally.
Whip the cream into soft peaks, then fold into the cooled chocolate mixture. Churn in an ice-cream machine, according to the manufacturer’s instructions, until it’s frozen.