Layer the stew. Put the chicken thighs in the bottom of a 6-quart slow cooker. Add the broth, carrots, celery, onion, garlic, thyme, bay leaf, salt, and pepper. Stir once to combine.
Cook low and slow. Cover and cook on LOW for 6 to 7 hours, or on HIGH for 3 to 4 hours, until the chicken is tender enough to shred with a fork and reads 165°F on a thermometer.
Shred the chicken. Lift the thighs out, shred them with two forks, and return the meat to the pot. Fish out the bay leaf. Stir in the heavy cream.
Bring it to a simmer. Turn the slow cooker to HIGH and let the stew heat for 15 minutes. The surface needs to be visibly bubbling before the dumplings go in — this is the step that decides whether they puff or sink.
Drop the dumplings. Cut each biscuit into quarters and drop the pieces across the surface of the simmering stew, spacing them out. Press them gently into the broth but do not stir them in.
Lid on, no peeking. Cover and cook on HIGH for 45 to 60 minutes, undisturbed. The dumplings are done when they are puffed up and a toothpick inserted in the center of one comes out clean. If you are adding peas, stir them in during the last 10 minutes.
Serve. Ladle into bowls, dumplings on top, and scatter with parsley.
