If using raw pork shoulder, season with salt and pepper. Heat oil in a large Dutch Oven over medium. Working in batches if necessary, add pork and cook until brown on all sides, about 10 minutes total. Transfer pork to a Sheet Pan or Platter and set aside.

Discard all but 2 Tbsp. fat from Dutch Oven. (If using leftover cooked pork, add 2 Tbsp. oil here.) Add onion and garlic. Season with salt to taste, 1 Tbsp. pepper, and cumin. Sauté until fragrant, about 2 minutes.

Add chiles to Dutch Oven and deglaze bottom, scraping pot to release browned bits. Add pork and stock and season with salt. Stir to combine. Bring pot to a simmer, cover, and decrease heat to low.

If you started with raw pork shoulder, continue cooking over low until all vegetables are softened, pork is tender and falling apart, and flavors have melded together, about 2 hours. Check on it periodically and add more stock if mixture starts to look dry. If you used leftover cooked pork, your stew will come together in about 20 minutes. Taste and adjust seasoning.

Ladle into bowls, garnish with a squeeze of lime juice, and top with cilantro. Serve with warm flour tortillas.