Peel and chop onion, smash and peel 6 cloves of garlic and mince 6 cloves of garlic. Set aside.
Using a sharp knife, cut pork into large chunks. Remove any visible excess fat and discard.
Place trimmed chunks of pork in the bottom of a large dutch oven pot and cover with water. Add just enough water so that the meat is submerged under about an inch of water.
Add half the chopped onion, the 6 smashed garlic cloves, salt, pepper, cumin and oregano.
Stir and bring mixture to a boil over high heat.
Once the mixture comes to a boil, reduce heat and cover pot. Simmer mixture over low heat for 45 minutes.
Use a spoon to skim off any foam that rises to the surface of the broth.
Using tongs remove the pork meat from the pot.
Use an emersion blender to puree the broth in the pot.
Cut pork into smaller bite sized pieces, about an inch in size. Discard bones. Use care, meat will be hot.
In a large skillet, heat 2 tablespoons olive oil over medium heat.
Sauté the remaining chopped onion and 6 cloves of minced garlic until onion is soft and translucent.
Add the reminaing spices; cayenne pepper, red chili powder, and ancho chili powder. Stir to coat onions and garlic with the spices. Cook until fragrant, about 1-2 minutes.
Add the cubed pork meat and sauté until meat pieces are browned. Cook in two batches if all the meat will not fit comfortably in the skillet.
Return the browned pork, along with the spices and diced onions to the pureed broth in the Dutch oven.
Stir in the drained and rinsed hominy, the can of diced green chiles and the chicken broth.
Increase heat and bring the mixture to a boil.
Once mixture comes to a boil, reduce heat to low and cover the pot.
Cook soup on low for 1½ to 2 hours, stirring occasionally.
Soup is done once pork meat is tender.
To serve soup, ladel a generous serving into a bowl. Be sure to include a generous amount of meat and hominy along with the broth. Top each bowl with chopped cilantro, shredded cabbage, dried Oregano, diced onion, and a squeeze of fresh lime juice.