Whisk the condensed soup and broth in the slow cooker until smooth.
Stir in onion, celery, carrots, garlic, butter, thyme, poultry seasoning, salt, and pepper.
Nestle chicken breasts into the mixture and spoon sauce over top.
Cover and cook on Low 5–6 hours or High 3–4 hours, until chicken shreds easily.
Transfer chicken to a board, shred into bite-size pieces, then return to the cooker.
Stir in the heavy cream to enrich the sauce.
Mix cornstarch and water, then stir the slurry into the pot to thicken.
Add biscuit pieces, pressing gently to submerge without stirring hard.
Cover and cook on High 60–90 minutes, stirring once, until dumplings are set and not doughy.
Fold in peas and parsley. Cook 5–10 minutes more. Rest briefly, then serve.