Soak beans overnight and rinse them. Alternatively, parboil them, remove from heat, allow them to soak for one hour in the hot water, and then drain and rinse them.
Add beans back to the pot or Dutch oven and add enough water to cover the beans by at least 1 inch.
Add beef shortribs, quartered onion, garlic cloves, bay leaves, and Mexican oregano to the pot.
Take off the stems and remove the seeds of the guajillo and ancho peppers, then add them to the pot as well.
Bring to a boil and reduce to a simmer. Cook for 3 hours before the next step. Check periodically and add more water if too much has boiled away.
At the 3 hour mark, remove the bay leaves and set them aside. Remove the chiles, onions, and garlic cloves and place them in a blender.
Blend until a smooth paste forms, adding some of the cooking water if needed to get it to a more liquid-y consistency.
Pass the paste through a sieve or (more easily) through a food mill. Pour this smoothed out sauce back into the pot and stir.
At the 3.5 hour mark (or when the meat is fork-tender and fall-off-the-bone), remove the meat and allow to cool.
Once it’s cool enough to handle, shred it with fingers or forks; using fingers makes it a little easier to remove excess fat.
At the 4 hour mark, return shredded meat to the pot and add the 25oz. can of hominy, and allow both to get warmed through. Add salt to taste.
Serve with optional garnishes. Like the pozole blanco de res version, the flavors and textures improve overnight and make great leftovers.