Sauté the vegetables: Heat the oil in a large pot over medium heat. Add onion and bell pepper, and cook 4–5 minutes until softened.
Stir in the garlic and cook 30 seconds until fragrant.
Bloom the spices: Add cumin, oregano, chili powder, and cayenne. Stir for 30–60 seconds to release their aroma.
Add chiles and broth: Stir in the green chiles and chicken broth. Bring to a gentle simmer.
Stir in the chicken: Add shredded chicken.
Simmer 10 minutes to meld flavors.
Make it creamy: Reduce heat to low. Stir in cream cheese until melted and smooth, then add heavy cream.
Cheesy finish: Sprinkle in Monterey Jack, stirring until fully melted. Do not boil after adding cheese to avoid separation.
Season and brighten: Add cilantro, lime juice, and season with salt and pepper.
Adjust heat with more cayenne if desired.
Serve: Ladle into bowls and top with jalapeño, avocado, extra cheese, and sour cream if you like.