Rinse the hominy thoroughly until the water runs clear (you can find hominy at Latin grocery stores or online). Boil the hominy for about 20 minutes if using canned, or 40 to 70 minutes if using dried.

In a separate large pot, add the onion (cut into 4 pieces), pork, and garlic. Cover with 15 cups water (about 3.5 liters) and simmer for about 1 hour, until the meat is tender. Skim off any foam that forms on top.

Remove the meat from the pot after an hour and shred or chop it as you like. Do not discard the broth.

Boil 2 cups water separately. Add the guajillo chiles (stems and seeds removed), garlic, and the onion you removed from the broth. Blend everything well, then add it back to the meat broth.

To serve, top the soup with thinly sliced radishes, shredded cabbage, lime wedges, fried corn tortillas or tortilla chips, chopped red onion, and a sprinkle of oregano. Add the fresh vegetables on top for crunch. Pozole can be made a day ahead and frozen if you have leftovers.