Prepare the onion, peel the garlic, chop the onion, peel and chop the 2 garlic cloves, chop the green chilies and jalapeños if you are using them and get the hominy drained and rinsed.
Place the meat in a large pot and just cover with lightly salted water.
Add 1/2 chopped onion, the 2 cloves peeled garlic, pepper, cumin, and oregano.
Bring to a boil over medium heat, skim off any foam that rises, reduce heat, cover and simmer for 45 minutes.
Remove meat and broth, reserving both.
Sauté the remaining chopped onion and garlic in oil until translucent.
Add the remaining spices, stir for a minute.
Cut the reserved pork into 1 inch cubes and add to the pan.
Stir in the canned hominy, pork broth (if there is not enough pork broth, add chicken stock, I like to add it anyway for flavor, about 2-4 cups, eyeball the amount you like), green chilies and jalapeños.
Cook at a simmer, covered, for 2 hours until the meat and hominy are tender.
Degrease the stew, taste for salt, and serve in soup bowls.
This is a delicious recipe and well worth the effort to make.