In a heavy saucepan, combine sugar, milk, and corn syrup. Bring to a boil, reduce heat, and simmer 5 minutes. Pour this liquid over marshmallows and, with a hand-held mixer, whisk, or egg beater, beat until smooth. Sauce will thicken as it cooks. Remove from heat. Add vanilla. Serve at room temperature.
Makes enough for 4 to 6 sundaes.