Add the chicken thighs, chicken broth, carrots, celery, onion, parsley, and black pepper to the slow cooker.
Cover and cook on low for 6 hours until the chicken is tender and the vegetables are soft.
Remove the chicken, shred it with two forks, and return it to the slow cooker.
In a medium bowl, stir together the flour, baking powder, salt, milk, and melted butter until a thick batter forms.
Drop spoonfuls of the batter directly onto the surface of the hot soup.
Cover and cook on high for 1 hour until the dumplings are cooked through and no longer doughy in the center.