Prepare the white beans as described below, (rinsing and soaking for 48-72 hours), before starting the main chili recipe. (For a dairy-free version, see Variations below.)
Place white beans in a large bowl or pot. Add water to cover by a couple of inches. Soak 18-24 hours, then change water and repeat. (Add an optional piece of kombu if desired.) Soak beans as long as 3 to 4 days, total, changing the water and rinsing the beans and bowl each time. Soak the beans until no more bubbles have risen to the water's surface after a soaking.
Place rinsed, soaked beans into empty Crock Pot or Instant Pot insert.
Add the following: bone broth, chicken, green onions, green chilies, fat, garlic, spices and sea salt. For Crock Pot: Stir and set heat on low for 8 hours. For Instant Pot: Press "Stew" button, seal lid, shut steam valve, and allow pressure to release naturally after cooking time has elapsed.
After cooking: Remove 4 cups of flavorful broth, beans, chilies and onions, taking care to leave chicken in pot. Allow this to cool slightly, about 20-30 minutes. Meanwhile use two forks to quickly break up/shred the chicken thighs into bite-size pieces. (They almost fall apart.)
Puree slightly-cooled broth and beans for 50 seconds, until smooth. Add puree back into crock pot. (Always use caution when pureeing hot liquid.)
When ready to serve, add cream and cheese. Stir and serve. Garnish bowls with sour cream, grated cheese and thinly sliced green onion, according to preference.