Bring 1 cup water and sugar to a boil in a saucepan over medium-high heat, stirring until sugar dissolves. Remove mixture from heat; cover and chill 25 minutes.
Stir together chilled sugar syrup mixture, 2 cups buttermilk, grated lime rind, and next 3 ingredients. Pour mixture into freezer container of a 2- or 4-quart ice-cream maker, and freeze according to manufacturer's instructions. Garnish, if desired.