Gather the ingredients.
Cut the pork into chunks. Fairly big pieces are traditional, but if you prefer, cut the pork into bite-sized pieces.
Put the pork in a large pot and add enough cool water to cover it by about 2 inches (approximately 5 to 6 cups). Bring to a boil, skimming off any foam that forms in the pot.
Remove the stem and seeds from the chiles, and peel the garlic. Add the chiles, garlic, and salt to the pork.
Reduce the heat to maintain a steady simmer, cover, and cook until the pork is fork tender, about 90 minutes. Alternatively, put the covered, ovenproof pot in a 350 F oven for the same amount of time.
After the pork has cooked, add the hominy and the Mexican oregano. Continue cooking at a simmer until the flavors blend and the pork is very tender, for another hour. Add additional water, if necessary, to keep the moisture at a good level, return the mixture to a boil and reduce back down to a simmer when needed. Add salt to taste.
Serve the pozole in deep bowls.
Garnish with chopped cilantro, scallion, radish, and green cabbage. If you like, squeeze fresh lime juice on top. Enjoy.