In a saucepan heat the milk and cream to scalding. Chop the chocolate into small pieces. Remove the milk and cream from the heat. Add the chopped chocolate, stir until completely melted. In a large bowl, using a whisk, beat the sugar with the egg yolks and vanilla extract until the mixture is light and fluffy. Gradually pour the hot chocolate mixture into the egg mixture, whisking constantly.
Heat the mixture in a bowl over simmering water, stirring constantly with a whisk or wooden spoon, until it thickens enough to coat the spoon.
Let cool to room temperature, refrigerate, covered, until completely cold, preferably overnight. Process the mixture in an ice cream freezer following the manufacturers instructions. Serve immediately.