1. Pat pork dry and season with some salt and pepper. Brown in oil in uncrowded batches, about 5–7 minutes each. Transfer to a plate.
2. Cook onion over medium heat 4–5 minutes. Add garlic and dried spices; stir 30 seconds.
3. Add chiles and broth. Return pork and juices, scrape browned bits, and bring just to a boil.
4. Simmer gently, partially covered, approximately 1½–2 hours or longer until fork-tender. Add broth as needed.
5. Add beans and corn; simmer about 10 minutes until heated through.
6. Whisk masa with cool water. Stir into the simmering base and cook 8–10 minutes, stirring along the bottom.
7. Reduce heat to low. Stir in milk, cream, and cream cheese gradually until incorporated. Avoid boiling.
8. Add Monterey Jack a handful at a time over very low heat or off the burner, stirring until melted.
9. Add cilantro and lime to taste. Adjust salt and consistency, then serve with optional toppings.

Storage: Refrigerate promptly and use within 3–4 days. Freeze the base without dairy for up to 3 months for quality. Reheat leftovers to 165°F.

Little tip: Finish the pork and masa cooking before adding dairy. The queso stage needs gentle warmth, not the long simmer that tenderizes shoulder.