Season the chicken breasts generously with salt and pepper. Poach, bake, or pressure cook them until fully cooked (internal temperature 165°F). Once cooled slightly, shred the chicken using two forks and set aside.

In a large Dutch oven or pot, heat olive oil over medium heat. Add the chopped onion and sauté until softened and translucent, about 5-7 minutes.

Add the minced garlic, ground cumin, dried oregano, and cayenne pepper (if using). Cook for 1 minute until fragrant, stirring constantly to prevent burning the spices.

Stir in the rinsed cannellini beans, undrained green chiles, and chicken broth. Bring the mixture to a low simmer, scraping up any browned bits from the bottom of the pot.

Reduce heat to low. Add the cubed cream cheese one piece at a time, stirring until completely melted and incorporated into the broth to create a creamy base. This should take about 5 minutes.

Stir in the shredded chicken. Continue to simmer gently for another 10 minutes, allowing the flavors to meld. Season with salt and freshly ground black pepper to taste.

Remove the pot from the heat. Stir in the shredded Monterey Jack cheese until fully melted and smooth. Serve hot garnished with sour cream, fresh cilantro, and avocado, if desired.