Put the honeydew, liqueur, lime juice, basil, salt and 2 tablespoons of the sugar in a blender and puree until the basil is fairly fine. Taste, and if you would like it a little sweeter, blend in the remaining tablespoon sugar. Pour into an 8- or 9-inch square metal baking dish and freeze until slushy, 30 to 40 minutes. Scrape with a fork and spoon into cold glasses or small bowls.
Copyright 2013 Cooking Channel, LLC. All rights reserved.