Combine sugar, 1 cup juice, and corn syrup in a medium saucepan over medium-high heat. Cook 2 minutes or until sugar melts, stirring constantly. Stir in basil. Cook 30 seconds. Remove from heat. Pour mixture into a bowl. Add remaining 1 cup juice, 2 cups water, and 1 tablespoon rind. Cover and chill. Strain mixture through a fine sieve; discard solids. Pour mixture into a freezer can of an ice-cream freezer; freeze according to manufacturer's instructions. Spoon mixture into a freezer-safe container; cover and freeze 1 hour or until firm. Garnish with finely grated rind, if desired.