Cut the pork roast into 2" chunks, removing any large pieces of fat. You want to keep a little bit of the fat for flavor.
Sear the pork pieces in the Instant Pot or stove-top. If you want to sear the pork in the instant pot, do this before you cook the hominy and then remove the pork to a plate. Searing will add more flavor to the over-all dish. But to stream-line the recipe, this most certainly can be made without this step.
Add soaked hominy and water it soaked in, to the pressure cooker.
Close and lock the lid of the pressure cooker.
Cook for 15 minutes at high pressure.
When time is up, release the pressure through the release valve, then open.
Add the pork pieces, bay leaves, dry Guajillo chilies, oregano, cumin powder, garlic, and salt.
Close and lock the lid of the pressure cooker and cook at high pressure for 10 minutes.
When the 10 minutes is up, natural release for 25 minutes. Once the 25 minutes is up, press the release valve to finish the steam release. Open only if the pressure indicator has gone down.
Find and discard the bay leaf. Find the Guajillo chilies and remove them.
In a small chopper puree the dried chiles and two spoons of hominy into a paste. Add the paste to the pressure cooker. This step will thicken the soup.
Add the Roasted Hatch or Pueblo Chiles. You can also use canned chiles if you don't have access to roasted fresh chile.
Simmer the contents of the pressure cooker uncovered for 5-10 minutes or until the desired thickness is reached.
Serve ideas: flour tortillas, radish, avocado, cabbage, cilantro, chopped fresh sweet onion and lime.