Add the chicken, onion, carrots, celery, garlic, salt, pepper, thyme, and parsley to the slow cooker.
Pour in the chicken broth and add the butter. Cover and cook on LOW for 6–7 hours or HIGH for 3–4 hours, until the chicken is tender.
Remove the chicken, shred it with two forks, then return it to the slow cooker and stir to combine.
Whisk the milk with the flour until smooth. Stir into the slow cooker, cover, and cook on HIGH for 15–20 minutes, until the broth thickens.
In a medium bowl, mix together the flour, baking powder, and salt. Stir in the melted butter and milk just until combined.
Drop spoonfuls of dumpling dough directly onto the hot stew.
Cover and cook on HIGH for 30–40 minutes, until the dumplings are fluffy and cooked through. Do not lift the lid during this time.
Taste and adjust seasoning as needed. Serve warm.