Begin by cutting away large pieces of fat from the pork shoulder. You’re not looking to remove all the fat, just any large pieces that you know would not be fun to chew through later. If you have a bone-in cut, at this time you should also cut around the bone as much as you can, but keep it as we will use it in this recipe. It’s also totally fine to use pork shoulder that does not contain a bone.
Cut the meat into small cubes.
In a large pot or dutch oven over medium-high heat, lightly brown the meat. You are not aiming to fully cook it, just get a good sear on the pieces.
Turn the heat down to medium-low and add the whole garlic cloves, chopped onion (cut into large pieces, to remove later), bouillon cube and five cups of water.
Cover and allow to simmer for 1 hour. If you notice a lot of foam or fat rising to the top, skim this off.
Cut off the tops of the dried chiles and remove the seeds. In a small pot, boil one cup of water and add the chiles. Boil for 5 minutes, then cover the pot and turn the heat off and allow it to continue to cook and cool for 5 minutes. Then blend/puree in a food processor or blender until smooth.
Once the broth has cooked for the initial hour, uncover the pot and remove the garlic, onion pieces and the pork bone.
Strain the chili mixture through a fine mesh sieve into the pot.
Then add the tomato sauce, oregano, cumin, and the drained hominy kernels. Continue to cook for another 15 minutes. Taste and add any salt and pepper you feel it needs.
Serve hot and garnish with shredded green cabbage, thinly sliced radish, fresh cilantro and lime juice. I also like to serve with a few warmed flour tortillas for dipping and sopping up the liquid from the soup.