Add the onion, garlic, bay leaves, salt, cumin, black pepper, Mexican oregano, and 2 cups of chicken broth to a large blender. Blend until smooth.
In a large pot or Dutch oven, combine the blended onion mixture, pork, hominy, and the remaining 2 cups of broth. Bring to a boil over high heat, reduce heat to low, cover, and simmer for 3 hours or until the pork is fall-apart tender.
Remove the pork from the pot and transfer it to a large bowl. Shred it with a fork or tongs (it should fall apart very easily), then transfer it back into the pot.
Serve the pozole in bowls topped with thinly shredded cabbage, cilantro, lime juice, sliced radishes, diced onions, avocados, dried Mexican oregano, and some spicy salsa roja.
Notes
Mexican oregano: If you don't have Mexican oregano, you can use regular oregano instead. It will have a slightly different flavor, but the dish will still be delicious.
Hominy: If you can't find white hominy, you can use yellow hominy instead.
Meat: This dish is traditionally made with pork, but if you prefer chicken, I recommend using bone-in chicken thighs. The cooking time will also be much shorter, and you only need to cook it for about 30 minutes once it boils, until the chicken is cooked through.