In a small saucepan, combine the sugar and water and bring the mixture to a boil. Add the basil leaves and blanch just until wilted, about 30 seconds. Let cool slightly, then transfer the mixture to a blender and puree until smooth. Let the puree cool. In a medium bowl, stir the basil puree into the vanilla ice cream; leave visible streaks in the ice cream. Freeze the basil ice cream until firm.