Cook the pork. Heat a large Dutch oven over medium-high heat, then add and heat the vegetable oil. Add the pork pieces and sear on all sides until browned. Do this in batches if you have to, for me it took 2 batches. Add all the pork back to the Dutch oven, including any juices, the 4 quarts of water and the bay leaves. Bring to a boil, cover with a lid, reduce the heat to medium-low and cook for 1 hour. Check the broth occasionally to see if there are any impurities at the top, if there are make sure to remove them using a slotted spoon. This is important to ensure we get a nice clear broth.
Prep the dried chiles. In the mean time, remove the stems and seeds from all the dried chiles. Add the chiles to a pot with boiling water and let them soak for 30 minutes.
Make the chile sauce. After 30 minutes, transfer the chiles to a blender, along with onion, garlic, oregano, cumin and 1 to 2 cups of the chicken broth. Pulse a few times until completely pureed.
Stir in chile sauce and cook. After the pork has been cooking for 1 hour, add the rest of the chicken broth and the chile sauce. Bring to a boil again, cover with a lid and cook for another 30 minutes. If too much of the water evaporates, add a bit more.
Add hominy and cook. Add the hominy to the pot, give it a good stir and cook for another 30 to 45 minutes. Alternatively you can first transfer the meat from the pot and shred it, especially if you cut the pork in bigger pieces, then add it back to the pot.
Serve with favorite toppings. Serve with shredded cabbage, chopped onion, radish slices and a wedge of lime.