In a medium saucepan over medium-low heat, combine the chocolate with the heavy cream, granulated sugar, and milk. Cook, stirring, until the mixture is hot and sugar has dissolved. Do not let the mixture boil.

Whisk the eggs in a small bowl and then whisk in about 1 cup of the hot mixture. Return the egg mixture to the saucepan and continue cooking over low heat, stirring, until the mixture coats a spoon or reaches a temperature of about 170 F to 180 F. Cover and chill thoroughly.

Freeze the chilled custard in an ice cream freezer, following the manufacturer's directions.

Pack the ice cream into a container; cover and freeze.