Layer the slow cooker: Place the raw chicken breasts flat across the bottom of a 6-quart slow cooker. Scatter the diced onion, minced garlic, diced mild green chiles, corn, and 1 can of the rinsed cannellini beans evenly over the chicken.
The secret thickening step: In a small bowl, roughly mash the second can of cannellini beans with a fork or potato masher until paste-like. Add the mashed beans to the slow cooker (this naturally thickens the chili broth without excess flour or heavy starches).
Add spices & broth: Sprinkle the ground cumin, oregano, chili powder, garlic powder, onion powder, smoked paprika, red pepper flakes, salt, and black pepper over the ingredients. Pour the 4 cups of chicken broth over everything and stir gently around the chicken to distribute the seasonings.
Slow cook: Cover with the lid and cook on LOW for 6 to 7 hours or on HIGH for 3.5 to 4 hours, until the chicken is exceptionally tender and shreds effortlessly with a fork.
Shred the chicken: Transfer the cooked chicken breasts to a cutting board or shred them directly inside the slow cooker using two forks into bite-sized shreds. Return the shredded meat to the broth.
Whisk in the cheeses: Add the cubed softened cream cheese, heavy cream, and 1 cup of the shredded Monterey Jack cheese to the hot chili. Stir continuously until the cheeses melt completely into the warm broth, creating a luxurious, velvety, creamy sauce. Stir in the fresh lime juice and let rest on WARM for 10 minutes to thicken.
Garnish & serve: Ladle generous steaming bowls of white chicken chili. Top with remaining Monterey Jack cheese, a dollop of sour cream, sliced avocado, fresh jalapeño coins, cilantro, and a mountain of crispy tortilla strips. Serve hot with warm skillet cornbread!
