Season the head or shanks lightly with salt and pepper and roast in a 350 F oven for 45 minutes.
In a stock pot large or wide enough to fit the head, sweat the onion and garlic for 5 minutes until translucent. Add the head, hominy, stew meat, bay leaves, dried oregano, water, cover and bring the mixture to a low simmer, then cover and cook for 3-4 hours.
The head will not be completely covered with water, so you’ll need to turn it occasionally to ensure even cooking.*
Put the guajillo chilis in a blender or food processor with 1.5 cups hot stock from the posole, and puree until smooth, then add back to the pot.
When the meat is tender and the hominy has started to pop, remove the head and cool on a cutting board. Using gloves, remove the meat from the head when cool, including the tongue, and chop coarsely, peeling the tongue beforehand.
Add the chopped meat back to the soup, season to taste with salt, then serve, garnished with lime, avocado, cilantro and radishes.