Line a large, rimmed baking sheet with aluminum foil (for easy clean up) and place the chicken on the foiled coated with cooking spray. Sprinkle with salt (and pepper), if desired. Bake for 25 minutes or until the chicken reaches 165 degrees with an instant read thermometer.
Meanwhile, chop the onion and garlic. Cook the onion and garlic in 1 tablespoon oil in an 8 quart pot over medium heat, stirring often until onion is almost tender.
Add chicken broth to deglaze the pan then add the green chiles, cumin, oregano, and salt.
When the chicken is done, place the breasts on a cutting board and shred by pulling it apart with two forks. You may have to cut some of the pieces into bite size pieces. Add the chicken to the soup mixture. Cover and bring to a boil over medium-high heat. Reduce heat to a simmer and simmer 15 minutes.If you prefer a more creamy texture, partially mash the beans with a potato masher right in the pot.
Serve in bowls and top with cheese and if desired a squeeze of fresh lime, cilantro and sour cream.
Additional shortcut: I often use Rotisserie chicken and chop or shred it.