Puree cucumbers with water, vinegar, and 2 teaspoons kosher salt in batches in a blender until smooth.
Mash together avocado, lime juice, and remaining teaspoon kosher salt until smooth. Whisk in yogurt, wasabi paste, chives, and pepper, to taste.
Just before serving, blend soup with ice in batches until smooth. Serve topped with avocado cream.
Soup (before blending with ice) and avocado cream can be made 1 day ahead and kept, separately, chilled and covered.
Recipe courtesy of Gourmet Magazine