In a blender, combine half the cucumber and 1 avocado with the yogurt, lime juice, jalapeno, scallions, 1 tablespoon cilantro, 1 cup ice water, 1 1/2 teaspoons salt, and 1/4 teaspoon pepper. Puree until completely smooth. Transfer to a large bowl.
Cut remaining avocado into 1/4-inch cubes. Stir avocado and remaining cucumber into soup. Thin with 1/2 to 1 cup ice water, as desired. Season again with salt and pepper. Chill, about 1 hour.