Place the chicken breasts in the bottom of your slow cooker.
Add the diced onion, minced garlic, green chiles, salsa verde, white beans, and chicken broth to the slow cooker.
Sprinkle in the cumin, oregano, chili powder, cayenne pepper (if using), salt, and black pepper. Stir gently to combine, making sure the chicken is submerged in the liquid.
Cover and cook on low for 5-6 hours or on high for 3-4 hours, until the chicken is cooked through and tender.
Remove the chicken from the slow cooker and shred it using two forks. Return the shredded chicken to the pot.
Stir in the fresh cilantro and lime juice. Taste and adjust seasonings if needed.
Serve hot topped with shredded Monterey Jack cheese, avocado slices, sour cream, and tortilla chips for dipping.