Place chicken in the bottom of a 6-quart [or larger] slow cooker.
Add broth, beans, green chilis, garlic, onion, cumin, oregano, salt and cayenne pepper. Stir to combine.
Cook on low for 4-6 hours or high for 2-4 hours, or until a meat thermometer inserted into the chicken reads 165°F.
Remove chicken breasts to a plate and shred with two forks. Set aside.
With an immersion blender, puree a portion of the soup to thicken, leaving some of the beans whole. Alternatively, scoop a few ladlefuls of soup into a food processor and blend. Stir the pureed/processed portion back into the soup.
Stir in the shredded chicken and cilantro.
Portion into serving bowls and top each with a squeeze of fresh lime juice. Add desired topping [if using] and enjoy.
Vegetarian version - swap 16 oz cubed tofu [sprouted, if possible] for chicken. Cook in slow cooker on high for 2 hours. Skip step 4. Serving size: 2 cups