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Bring pork, 5 cloves of garlic, salt and water to a boil.
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Reduce heat to low and simmer until pork is done. (about 2 hours)
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Remove meat from pot and let cool. When cool shred into smaller pieces.
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When broth has cooled strain and reserve.
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Toast the chilies on a skillet over medium heat for about 30 seconds. Transfer chilies to a pot with 2 cups of hot water.
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Let chiles soak for about 10-15 minutes.
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Transfer chilies and water, 3 garlic cloves and 1/4 white onion to a blender.
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Blend for a minute or two.
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Heat up 1 1/2 tbs of olive oil in pot over medium heat. When hot add in the blended chile sauce with a mesh strainer.
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Fry the sauce for a few minutes then add in the strained broth. Stir well.
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Next add the two cans of hominy (water drained).
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Simmer for an additional 20 minutes.
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Turn heat off and add in the pork pieces. Season with additional salt if desired.
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Serve and garnish.