For syrup, in a small saucepan combine sugar and the water. Bring to boiling over high heat, stirring to dissolve sugar. Reduce heat. Boil gently, uncovered, about 10 minutes or until reduced to 3/4 cup.
In a medium bowl combine warm syrup, orange peel, orange juice, basil, and, if desired, liqueur. Cover and let stand for 1 hour. Strain mixture through a fine-mesh sieve into a bowl; discard basil. Cover and chill strained mixture about 2 hours or until well chilled.
Freeze mixture in a 2-quart ice cream freezer according to the manufacturers directions. If desired, ripen for 2 to 4 hours.