Heat oil in a Dutch oven over medium high heat until just smoking.
Add onion and ½ teaspoon each salt and pepper. Saute until softened, about 5 minutes. Add garlic and oregano. Stir until fragrant, about 30 seconds to 1 minute.
Add pork and bones and cook, stirring often until the pork is no longer pink on the outside.
Add chicken stock and green enchilada sauce. Scrape up any brown bits on the bottom of the pan. Stir in potatoes.
Cover with a tight fitting lid and transfer to the oven. Cook until the pork is tender, about 2 hours.
Remove from the oven. Remove pork and shred with 2 forks.
Add hominy and green chiles. Bring to a simmer uncovered over medium heat for about 10 to 15 minutes.
Add fresh cilantro, lime juice and shredded pork back to the pot and cook just until heated through.
Season to taste with salt and freshly ground black pepper. Garnish with cilantro.
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NOTES: Thicken the broth if desired. Whisk 2 to 3 tablespoons of cornstarch in with 3 tablespoons of water and stir into the stew. Simmer until desired thickness is reached.
SERVING SUGGESTIONS: Adjust salt and pepper to taste. Garnish with cilantro, cubed avocado, green onion, cotija cheese, or sour cream. Serve with warm tortillas.