Whisk the miso into the chicken broth in the crock pot. Add the mushrooms, scallion whites, garlic, and ginger. Season the pork with pepper, place it in the crock pot, and cook until very tender and about 195°F 4–6 hours on high or 8–10 hours on low.
Transfer the pork to a cutting board and let it rest for 20 minutes. Remove the ginger and garlic.
Cook the ramen noodles in a large pot of boiling water until tender but still slightly chewy, then drain.
Slice the pork into thin pieces. Divide the noodles into bowls, ladle the hot broth over top, and finish with the sliced pork and scallion greens.
