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1
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.
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2
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.
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3
Shred pork and chicken into small chunks. Add salsa to the pot. Let soup simmer for 15 to 30 minutes more.
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4
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.
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5
Serve with cabbage, yogurt, cilantro, and radishes to garnish.
