Heat oil in a large pot or Dutch oven (see note) over medium heat. Add onions, carrots, celery and sauté until soft, about 5 minutes. Stir in garlic and all spices, and cook until fragrant, for about 1 minute.
Add chicken, green chili, broth, and cover with the lid. Once the soup starts boiling, reduce heat and simmer, covered, for 18–20 minutes, until chicken is tender and cooked through.
Meanwhile, using a fork, mash half of the beans and set aside. The remaining beans will be left whole to give texture to the soup.
Transfer the chicken to a plate and shred with two forks. Return the shredded chicken to the pot and stir in whole beans, mashed beans and corn. Continue to simmer for 5–7 minutes and allow all flavors to meld nicely. Turn heat off and stir in cheese cream, lime juice, and cilantro.
Ladle chili into bowls. Add toppings of choice and enjoy while hot!