Heat milk over medium-high heat in a small, heavy saucepan to 180° or until tiny bubbles form around edge (do not boil). Gradually add hot milk to sugar mixture, stirring constantly with a whisk. Place the milk mixture in pan, and cook over medium heat until very thick and bubbly (about 5 minutes), stirring constantly. Spoon mixture into a medium bowl, and add liqueur, vanilla, and chocolate, stirring until chocolate melts. Place bowl in a large ice-filled bowl for 15 minutes or until mixture is cool, stirring occasionally.