Mix together all of the spices and set them aside.

In a large soup pot, warm the butter and olive oil over medium heat. Add the onions and peppers and cook until softened, about 4 minutes. Stir in the garlic and cook for another minute.

Pat the chicken dry, season both sides with salt and pepper, and place it into the pot. Add the rest of the ingredients, reserving the cream cheese and shredded cheese for later.

Bring the soup to a light boil and let the chicken gently cook through, about 15–20 minutes (avoid a rolling boil to keep it tender). Remove the chicken, shred it with two forks, and return it to the pot.

Lower the heat, then mix in the softened cream cheese until smooth. Stir in the shredded cheese until fully melted.

Ladle into bowls and finish with your favorite toppings like sour cream, cilantro, or extra cheese.