In a medium saucepan over medium heat, combine sugar and water. Stir until mixture comes to a boil; boil 1 minute. Remove from heat.
In a food processor or blender, puree lime juice, sugar mixture, and chopped basil leaves.
Ice Cream Maker - Transfer mixture to ice cream maker, process according to manufacturer's instructions.
Freezer Method - Pour into container, cover, and place mixture in the freezer. When it is semi-solid, mash it up with a fork and refreeze again. When frozen, place in a food processor or blender and process until smooth. Cover and refreeze until serving time. When ready to serve, use a melon baller and place 3 scoops in a stemmed glass. Garnish with a sprig of fresh basil and serve.
Can be prepared 3 days in advance. Cover and keep frozen.
Makes 8 to 10 servings.
Lime Basil Sorbet Recipe https://whatscookingamerica.net/SorbetBasil.htm