Heat the olive oil in a large pot or Dutch oven over medium heat.
Add the diced onion and sauté for about 5 minutes, until it becomes translucent.
Stir in the minced garlic and cook for another 1-2 minutes, until fragrant.
Add the shredded chicken, white beans, chicken broth, diced green chiles, cumin, chili powder, oregano, cayenne pepper (if using), salt, and black pepper to the pot. Mix well to combine.
Bring the mixture to a gentle simmer and cook for about 20 minutes, stirring occasionally.
Remove the pot from heat and stir in the sour cream and half of the shredded cheese until well blended.
Taste and adjust the seasoning if necessary.
Serve hot, garnished with chopped cilantro and a squeeze of lime juice. Offer extra cheese on the side if desired.