Add chicken, onion, carrots, celery, garlic, broth, butter, salt, pepper, thyme, parsley, poultry seasoning, and bay leaf to a slow cooker.
Cook on LOW 6–7 hours or HIGH 3–4 hours, until chicken is tender.
Remove chicken, shred, return to slow cooker, and stir.
Optional: stir in a slurry of cornstarch + cold water. Cover and cook on HIGH 10–15 minutes to thicken.
Make dumplings: whisk flour, baking powder, and salt. Cut in cold butter until crumbly. Stir in milk just until dough forms. Fold in parsley if using.
Drop dough by tablespoonfuls on top of the hot broth.
Cover and cook on HIGH 45–60 minutes without lifting the lid.
Optional: stir in heavy cream during the last 5 minutes. Taste and adjust seasoning. Serve hot.