Season the chicken breasts evenly on both sides with the chili powder, cumin, salt, smoked paprika, black pepper, and cayenne pepper.
Place the chicken in the bottom of a 6-quart or larger slow cooker. Top with the diced onion, minced garlic, white beans, green chilis, corn, salsa verde, and broth. Stir to combine.
Place the lid on the slow cooker and cook on low heat for 6-8 hours, or high heat for 3-4 hours.
Turn the slow cooker to HIGH (if you had been cooking on low). Remove the chicken and shred, while keeping the slow cooker covered.
In a small bowl whisk together the cornstarch with the cold milk or water until smooth.
Remove the lid from the slow cooker and return the chicken, then, whisk in the cornstarch mixture.
Continue cooking on high for 15-20 minutes until thickened.
Add the sour cream to a medium bowl and stir in one ladle full of the liquid from the soup, then stir the sour cream mixture back into the soup.
Stir in the cream cheese until melted.