Drain and rinse the beans to remove excess salt. Place half the beans in a blender or food processor with some water and process until blended, but still slightly chunky. Transfer the puréed beans to a 5 or 6-quart slower cooker, along with the remaining whole beans.
Add chicken, red onion, garlic, green chilies, cumin, chili powder, Mexican oregano, coriander, chipotle pepper powder, and chicken broth to the slow cooker. Season with salt and black pepper, as desired, and stir to combine. Cover and set cook time to 4 hours on high or 8 hours on low.
When cook time is complete, remove lid and add 1 cup of the shredded cheese and stir to combine. Cover and allow cheese to melt for 1-2 minutes.
Taste and adjust seasonings, as desired. Serve immediately with remaining Mexican cheese, fresh cilantro, avocado, jalapeño slices, and/or lime wedges, if desired.