In a Dutch oven, brown chicken in butter; remove and set aside. In the same pan, combine the onion, celery, parsley, salt and pepper; cook and stir until vegetables are tender. Sprinkle with flour and mix well. Add broth and cider. Bring to a boil; cook and stir for 2 minutes or until thickened. Add chicken.
Cover and bake at 350° for 45-50 minutes. Increase heat to 425°.
For dumplings, combine the flour, baking powder and salt in a bowl; cut in butter until crumbly. Combine egg and milk; stir into dry ingredients just until moistened. Drop batter into 12 mounds onto hot broth.
Bake, uncovered, at 425° for 10 minutes. Cover and bake 10 minutes longer or until a toothpick inserted into a dumpling comes out clean.