Preparation Puree cucumbers, broth, feta, onion, mint, watercress, oregano, garlic, and salt in blender until smooth. Pour soup into large bowl; whisk in yogurt. Refrigerate until cold, about 2 hours. DO AHEAD: Soup can be made 1 day ahead. Cover; chill. Before serving, put soup in freezer 30 minutes. Pour into bowls; top with chopped egg and chives.
Preparation Puree cucumbers, broth, feta, onion, mint, watercress, oregano, garlic, and salt in blender until smooth. Pour soup into large bowl; whisk in yogurt. Refrigerate until cold, about 2 hours. DO AHEAD: Soup can be made 1 day ahead. Cover; chill. Before serving, put soup in freezer 30 minutes. Pour into bowls; top with chopped egg and chives.