Sauté the aromatics. Heat the olive oil or butter in a large pot over medium heat.
Add the onion, bell pepper, and jalapeño. Cook 4–5 minutes until softened. Stir in the garlic and cook 30 seconds until fragrant.
Toast the spices. Add cumin, chili powder, smoked paprika, and oregano.
Stir for 30–60 seconds to bloom the spices and deepen flavor.
Add the base. Stir in the potatoes, corn, green chiles, white beans, and chicken broth. Season with a pinch of salt and pepper. Bring to a gentle boil.
Simmer until tender. Reduce heat and simmer 12–15 minutes, or until the potatoes are just tender when pierced with a fork.
Stir in the chicken and cream. Add the cooked chicken and half-and-half (or cream/milk).
Simmer another 5 minutes to warm through. Do not let it boil hard once dairy is added.
Adjust thickness. For a thicker chowder, mash some of the potatoes and beans against the side of the pot. Or whisk 1 tablespoon cornstarch with 2 tablespoons cold water, then stir it in and simmer 2–3 minutes.
Finish with brightness. Stir in lime juice.
Taste and adjust salt, pepper, and chili powder as needed.
Serve and garnish. Ladle into bowls and top with cilantro or green onions. Add cheese, a dollop of sour cream, and tortilla strips if you like extra richness and crunch.