I actually haven't tried this one yet, but I'm looking forward to it.  The great thing about sorbet is that you don't need an ice cream maker - putting it in the freezer and taking it out for stirring every 30 mins or so works just as well.

Source: http://whatscookingamerica.net/SorbetBasil.htm

Lime-Basil Sorbet:

1 1/4 cups granulated sugar
1 cup water
1 cup (approximately 6 limes) freshly-squeezed lime juice
18 to 20 fresh basil leaves, finely chopped
Sprig of fresh basil for each serving as a garnish

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.

NOTE: Can be prepared 3 days in advance. Cover and keep frozen.

Makes 8 to 10 servings.