Preheat your oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Bring a large pot of salted water to a boil. Cook the egg noodles according to package directions until al dente. Drain and set aside.
While the noodles cook, melt 2 tablespoons of butter in a skillet over medium heat. Sauté the chopped celery and onion until tender and translucent, about 5-7 minutes.
In a large mixing bowl, combine the cream of chicken soup, sour cream (or milk), chicken broth, sautéed vegetables, poultry seasoning, and pepper. Stir until smooth.
Fold in the cooked chicken and the drained noodles, tossing gently to coat everything evenly with the sauce.
Transfer the mixture to the prepared baking dish, spreading it out evenly.
In a small bowl, mix the bread crumbs with the melted butter. Sprinkle this mixture over the top of the casserole.
Bake uncovered for 30-35 minutes, or until the casserole is bubbly and the topping is golden brown. Let stand for 5 minutes before serving.