This vegetarian soup offers guests a delightful sip of something bright and refreshing at your next summer affair.
Peel and seed cucumbers, reserving peels from 3 of them. Juice 2 cucumbers to yield 3/4 cup juice; set aside. Cut remaining 3 cucumbers into 1/2-inch dice, and place in a medium bowl. Add 1 1/2 tablespoons vinegar, the honey, and 1 teaspoon each salt and pepper, and toss. Let stand at room temperature 1 to 2 hours.
Prepare an ice bath; set aside. Bring a large pan of water to a boil; add salt. Add reserved cucumber peels and dill; blanch 2 minutes. Using a slotted spoon, transfer to ice bath for 1 minute; drain. Puree with 1 cup water in blender. Strain puree, discarding solids, and set liquid aside.
Place diced-cucumber mixture and avocado in the jar of a blender. Process to puree until smooth, and strain into a large bowl. Combine with reserved puree liquid and 1/2 cup reserved cucumber juice. Season with 1/4 teaspoon salt and a pinch of pepper. Chill in ice bath for 10 minutes, or refrigerate at least 1 hour.
In medium bowl, whisk yogurt and creme fraiche. Add corn syrup and remaining 1/4 cup cucumber juice and 1 1/2 teaspoons vinegar. Freeze in ice-creammaker according to maker's directions.
Serve chilled soup in twelve 2-ounce portions, each topped with a heaping tablespoon of yogurt sorbet.