Elderflower liqueur gives this granita a floral note, basil and lime keep it bracing. Serve it after the main course as a palate cleanser or as a light dessert. The recipe is easy to double; just puree in two batches. If you have extra time, top each bowl with a spoonful of diced melon.
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.
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