Bring 1 cup milk and 1/2 cup water to a boil in a medium saucepan. Reduce heat to medium. Combine sugar and cocoa, stirring with a whisk. Add sugar mixture to hot milk mixture, stirring with a whisk until blended. Bring to a simmer; simmer 5 minutes, stirring frequently. Remove pan from heat; add vanilla and chocolate, stirring with a whisk until chocolate melts. Pour milk mixture into 2 ice cube trays. Cool 30 minutes. Freeze 4 hours or until firm.
Place 4 chocolate ice cubes in each of 6 glasses; add 2/3 cup milk to each glass.