Rinse and remove the stem end and seeds from the dried New Mexico chilies.
Add chilies to a large bowl and cover with 3 cups of boiling water. Submerge and let soak for 30-45 minutes.
In a large stock pot, heat vegetable oil over medium heat. Sauté onion until translucent, then add minced garlic and cook until fragrant.
Add cubed pork stew meat to the pot and brown on all sides. Add chicken or vegetable stock to cover the meat.
Bring to a boil, then reduce heat and simmer until the pork is tender.
While the pork simmers, blend the soaked chilies into a smooth paste.
Add the chili paste, oregano, and thyme to the pot. Simmer for another 30 minutes.
Add the drained hominy to the pot and simmer for an additional 15-20 minutes.
Serve hot, garnished with diced white onion, chopped cilantro, shredded cabbage, and crushed red pepper flakes. Serve with lime slices, tortillas, and Mexican beer.