Cut or tear bread slices into bite-sized pieces.
Preheat oven to 350 degrees and butter a medium baking dish. In a large bowl, toss bread with 1/2 of the melted butter. Spread buttered bread in an even layer on a baking sheet and toast until golden and crisp, about 10-12 minutes.
Saute celery, onion and giblets in the remainder of the butter until soft, about 6 minutes.
Stir in seasonings.
Place bread in a large bowl and add skillet mixture. Toss to combine. In a medium bowl, whisk together chicken broth and beaten egg and pour over bread mixture.
Transfer mixture to the prepared baking dish and cover with foil. Bake until cooked through, 35 minutes, then remove foil and cook until bread is crisp on top, 15-20 minutes more.
Serve