Arrange bread cubes in a single layer on several ungreased large baking sheets. Bake at 350° for 20-30 minutes until golden brown and crisp.
Transfer to a large bowl. Stir in the chicken, potatoes, celery, carrots and parsley. In another large bowl, combine the milk, broth, eggs, butter, salt and pepper. Pour over bread mixture; toss to coat.
Pour into a greased 13x9-in. baking dish. Bake, uncovered, at 350° for 45 minutes; stir. Bake 45 minutes longer or until a knife inserted in the center comes out clean. Serve with gravy if desired.