• Measure seven quarts of water into a stockpot and add the pork shoulder and garlic, simmer for about one hour.
• Add in rinsed hominy and simmer, uncovered, for another 30 minutes.
• Meanwhile, tear the chilies in half, toast in a large cast-iron pan, pressing down on them all until they blacken and blister in places — about 30 seconds to one minute per side.
• Set in a bowl, cover with hot water and let soak for 30 minutes.
• Puree the chilies along with 1 1/2 cup of the soaking liquid and oregano.
• Strain into the soup, mix well. Season generously with salt.
• Let simmer another hour.
• Simmer until the pork is tender, then remove all of the pork pieces.
• Cool the meat, remove meat from bones, discard cartilage and bones. Shred the pork shoulder, reserve all of the meat.
• Re-season the soup with salt and lime juice.

To serve: Reheat the meat in the broth, ladle into large bowls, top with a small portion of the cabbage, radish, onion, and tortilla crisps. Serve with lime wedges.