Heat the olive oil in a large pot or Dutch oven over medium heat. Add the onion, garlic, and bell peppers and cook until softened, about 5-7 minutes.
Stir in the cumin, oregano, chili powder, and cayenne pepper (if using) and cook for 1 minute more, until fragrant.
Add the shredded chicken, chicken broth, cannellini beans, and great northern beans to the pot. Bring to a simmer and cook for 15-20 minutes, allowing the flavors to meld together.
Stir in the softened cream cheese until melted and smooth.
Stir in the cilantro and lime juice. Season with salt and pepper to taste.
Ladle into bowls and garnish with your favorite toppings.