- 2 cups water
- 1 cup sugar
- 1/3 cup packed fresh tarragon sprigs, crushed
- 2 cups (1-inch cubes) peeled seeded honeydew melon
- 2 lb chilled firm-ripe red or black plums, halved and pitted
- 2 teaspoons fresh lime juice, or to taste
- Special equipment: an ice cream maker
- Bring water and sugar to a simmer, stirring until sugar is dissolved. Transfer 1/2 cup hot syrup to a bowl and stir in tarragon, then cool. Chill remaining syrup.
- Pour tarragon syrup through a very fine sieve into a metal bowl, discarding solids. Purée honeydew in a blender and stir into strained tarragon syrup. Freeze in ice cream maker, then transfer to an airtight container and put in freezer to harden.
- Dice enough of plums to measure 1/2 cup and reserve. Coarsely chop remaining plums and purée in 2 batches with 1 cup chilled syrup (total) in a blender. Pour purée through very fine sieve into a bowl, pressing on and discarding solids.
- Stir in diced plums, lime juice, and chilled syrup to taste.
- Serve soup immediately, topped with scoops of honeydew ice.