Chop tomatillos coarsely. Purée half each of tomatillos, onion, and broth in a blender with garlic. Rub through a fine strainer into a stainless steel bowl; discard contents of strainer. Finely chop remaining tomatillos. Add remaining tomatillos, onion, and broth; cucumber; 2 tbsp. lime juice; 2 tsp. hot sauce; and the oregano to bowl and stir.
Nest bowl in ice water; stir often until cold, 15 minutes. Add avocado and cilantro and, if you like, more lime juice and hot sauce.
Note: Nutritional analysis is per 1-cup serving.