In a large Dutch oven, heat olive oil over medium-high heat.
Add onions, bell pepper, jalapeño, and garlic. Sauté until softened.
Place chicken breasts on top of veggies.
Add Cajun seasoning, cumin, oregano, onion powder, salt, pepper, and cayenne.
Stir in beans, green chiles, and chicken broth.
Bring to a boil, reduce heat to low, cover, and simmer for 25–30 minutes.
Remove the chicken, shred with two forks, and return it to the pot.
Add cream cheese and heavy cream, stirring until melted and smooth.
Simmer uncovered for 10 minutes to thicken.
Taste and adjust seasoning before serving. Garnish as desired.