Preheat oven to 350˚ F and grease a 13x9 casserole dish.
In a heavy-bottomed skillet, brown the bread crumbs in 2 Tablespoons butter over medium heat for 5 minutes or until golden. Set aside.
In a large skillet, sauté the celery, onion, and parley in ½ Cup of butter for five minutes. Add the cubed bread and toss. Add the salt, pepper, and poultry season and toss again. Add to the casserole dish and sprinkle with ⅓ cup chicken broth.
In a large skillet (4-5 quarts) melt 1 Cup of butter over medium-high heat. Add flour and stir until combined. Gradually add 4 cups of chicken broth and 1 cup milk. Whisking repeatedly. Add 1 teaspoon salt. Continue cooking over medium heat and stir constantly for 10 minutes or until thick.
Whisk the eggs in a small bowl. Add 1 cup of the hot broth mixture very slowly to the eggs in the bowl and whisk repeatedly. Add the egg mixture back to the hot broth. Cook over low heat for 3 minutes and stir.
Pour the thicken broth mixture over the prepared bread cubes in the casserole dish. Cover with the cooked chicken. Sprinkle with bread crumbs.
Bake at 350˚ F for 30-35 minutes or until bubbly and the center temperature reaches 160˚ F. Serve warm.