In a large saucepan, combine 3 cups of the milk, the sugar, and egg yolks. Cook and stir over medium heat until mixture just coats a metal spoon. Remove from heat. Stir in melted bittersweet chocolate. Use a wire whisk to whisk until milk mixture is combined and smooth. Whisk in the remaining 3 cups milk. Let cool for 20 minutes.
Cover surface of custard with plastic wrap. Chill for 6 to 24 hours. (Or place the saucepan in a sink of ice water. Let stand for 30 to 45 minutes or until cool, stirring occasionally.)
Stir in chopped dark chocolate and, if desired, white baking chocolate into chilled custard just before freezing. Freeze custard in a 4- or 5-quart ice cream freezer according to the manufacturer's directions. If desired, ripen for 4 hours.