In a large pot or Dutch oven, heat olive oil over medium heat.
Add the diced onion, carrots, and bell pepper. Sauté for 5-7 minutes until the vegetables are softened.
Stir in the minced garlic and cook for an additional minute until fragrant.
Add the chicken breasts to the pot, followed by the white beans, green chilies, chicken broth, cumin, oregano, chili powder, pepper, and salt. Stir well to combine.
Bring the mixture to a boil, then reduce the heat to low, cover, and simmer for about 20 minutes, or until the chicken is cooked through.
Remove the chicken breasts and shred or dice them, then return to the pot.
Stir in the sour cream and half of the shredded cheese until well combined.
Adjust seasoning if necessary, then serve hot, garnished with the remaining cheese and fresh cilantro if desired.