Arrange the chicken breasts across the bottom of the slow cooker.
Season the chicken evenly with the salt, black pepper, cumin, oregano, chili powder, and cayenne pepper.
Add the chopped yellow onion, minced garlic, drained Great Northern beans, diced green chiles, drained corn, chicken broth, and chopped cilantro.
Gently stir the ingredients together without disturbing the chicken more than necessary.
Place the lid securely on the slow cooker.
Cook on LOW for 8 hours. For a faster option, cook on HIGH for 3–4 hours.
At the end of the cooking period, transfer the chicken breasts from the slow cooker to a large bowl.
Using two forks, pull the chicken apart into bite-size shreds. Return all of the shredded chicken to the slow cooker.
Add the softened cream cheese and half-and-half to the chili.
Stir until incorporated, cover the slow cooker again, and cook on HIGH for an additional 15 minutes, allowing the mixture to become creamy and slightly thicker.
For an especially smooth consistency, place the softened cream cheese in a small bowl and whisk it with several ladlefuls of hot chili. Once smooth, stir the mixture back into the slow cooker along with the half-and-half.
Stir the finished chili thoroughly so the creamy ingredients and shredded chicken are evenly distributed.
Ladle the chili into bowls while hot and garnish as desired with grated Monterey Jack cheese, sliced avocado, jalapeños, tortilla strips, sour cream, or fresh cilantro.