First make the tomatillo salsa. Place the tomatillos, garlic cloves, roughly sliced onion, poblano and jalapeno on a baking sheet, cut side down. Broil while watching closely until blackened, approximately 5 -10 minutes. Set aside to cool for 15-20 minutes.
Once cool enough to handle, peel and discard the skin from the peppers. Puree everything, getting all the tomatillo juice that leaked everywhere with the cilantro. If you are sensitive to spice, test the salsa to see how much heat it has before deciding how much to add into the soup.
In a large pot add the broth, chicken, oregano and salsa and bring to a boil. Reduce heat and simmer until the chicken is cooked though, approximately 2-3 hours. (You can add everything to a slow cooker and cook on low for 6-8 hours or high 2-3 hours.)
Once the chicken is cooked, remove the chicken from the soup and add the hominey. Let the chicken cool until you can handle it, shred and add back into the soup. (NOTE - you can use pre-cooked, shredded chicken instead, add it in with the hominy and heat through. The flavor won't be as rich but you'll save several hours of cooking time.) Once everything is hot, add the lime juice and serve garnished with avocado, radishes, onion, cilantro, tortilla chips, cheese, sour cream...whatever you like!
This soup freezes well. Let it defrost overnight, heat and serve. For a vegetarian/vegan option substitute vegetable broth and black beans for the chicken.