"This is a flavorful, somewhat spicy version of New Mexican pozole soup made with readily available ingredients. A variety of peppers can be substituted to make it more or less spicy, according to your own tastes. We typically serve it with the listed garnishes, tearing the cilantro leaves from the stems right at the table (much like basil leaves and Vietnamese pho). The Greek yogurt is a healthier choice to sour cream, although sour cream would also be very tasty! Great fall and winter fare, served with warm tortillas or tortilla chips. (Leftovers are wonderful, but good luck with that!)"
Heat oil in a large pot over medium heat. Add pork, chicken, Hatch chile peppers, onion, jalapeno peppers, and garlic. Saute, turning meat, until lightly brown, about 8 minutes.
Pour 2 cups stock into pot; add enough water to cover meat by 3/4 inch. Bring to a boil. Reduce heat and simmer, covered, for 45 minutes. Remove pork and chicken and place on a plate; let cool until safe to handle. Remove garlic cloves, mash, and add back to soup.
Shred pork and chicken into small chunks. Add salsa to the pot. Let soup simmer for 15 to 30 minutes more.
Place hominy, shredded meat, remaining 4 cups stock, New Mexico chile powder, coriander, salt, and pepper into the pot of soup. Bring to a boil; reduce heat and simmer, uncovered, at least 30 minutes.
Serve with cabbage, yogurt, cilantro, and radishes to garnish.