For the best flavor, use high-quality chocolate, such as Ghirardelli or Guittard. Gourmet chocolate is available in the baking aisle at specialty food stores and many supermarkets.
Place 2 1/4 cups milk in a heavy saucepan; bring to a simmer over medium heat. Combine 1/4 cup milk, sugar, cornstarch, and salt in a medium bowl, stirring with a whisk until smooth. Slowly add the sugar mixture to pan, stirring constantly with a whisk. Cook 4 minutes or until mixture begins to thicken, stirring constantly with a whisk. Remove pan from heat.
Place chopped chocolate in a small bowl. Bring remaining 1/2 cup milk just to a boil in a small saucepan over medium heat. Pour hot milk over chocolate; let stand 1 minute. Stir chocolate mixture until smooth. Add chocolate mixture to sugar mixture; stir until well blended. Cover and chill 2 hours.
Pour mixture into the freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container; cover and freeze 1 hour or until firm.