Whisk together first 4 ingredients in a large saucepan until smooth. Bring to a boil over medium heat, whisking constantly; boil, whisking constantly, 2 minutes. Remove from heat. Cool slightly.
Stir in 6 cups cold milk, vanilla, and, if desired, liqueur. Cover mixture, and chill up to 2 days, or pour each serving immediately over 1/4 cup ice cream or ice cubes. Garnish, if desired.