FOR THE SORBET:
1 2–2 1/2-lb. ripe charentais or
cantaloupe melon, peeled, seeded,
and cut into chunks (to yield about 5 cups)
3–5 tbsp. superfine sugar
1. For the granita: Put lemon juice, sugar, and 5 tbsp. water into a bowl and stir until sugar dissolves completely. Pour into a medium glass baking dish and transfer to the freezer. Using the tines of a fork, stir the mixture every 30 minutes, scraping edges and breaking up any chunks as the mixture freezes, until granita is slushy and frozen, about 2 hours.
2. For the sorbet: Put melon and any melon juices and 3 tbsp. of the sugar into a blender and purée until smooth. Taste purée for sweetness (it should be slightly sweeter than the desired sweetness of the finished sorbet), adding more sugar, if you like. Pour purée into an ice cream maker and process according to the manufacturer's directions.
3. To serve, put a small spoonful of the granita in the center of a chilled shallow bowl, then put a samll scoop of the sorbet on top. Garnish with a sprig of tarragon, if you like.
MAKES 1 QUART SORBET AND 1 PINT GRANITA