Combine sugar and cocoa in a medium saucepan; add 1 cup milk, stirring with a whisk. Cook over medium heat 4 minutes or until hot. Gradually add about one-fourth hot milk mixture to eggs, stirring constantly with whisk. Add to remaining hot milk mixture, stirring constantly.
Add remaining 1 1/2 cups milk, half-and-half, and peanut butter, stirring with whisk until smooth. Cook 12 minutes over medium heat or until mixture reaches 160°, stirring constantly with whisk. Transfer mixture to a bowl. Cover and chill at least 1 hour, stirring occasionally.
Pour mixture into the freezer can of a 4-quart ice-cream freezer, and freeze according to manufacturer's instructions. Spoon ice cream into a freezer-safe container. Cover and freeze 2 hours or until firm.