Preheat oven to 325. Spray a 9 x 13 pan with cooking spray.
Cook celery and onion in 2 tablespoons of the butter over medium heat. Cook for about 5 minutes, or until softened. Add the kielbasa to the skillet and give it a brief toss. Add the rest of the stick of butter to the pan and let the butter melt completely, set it aside.
In a large mixing bowl, add the bread pieces, followed by the seasonings and eggs. Add the celery and onion mixture and mix all the ingredients together. Add about half of the chicken broth, and stir gently to combine. If the stuffing looks too dry, add more broth, 1/4 cup at a time. The stuffing should look moist, but not soggy.
Scoop the stuffing into the 9 x 13 pan. Cover with foil and bake at 325ºF for 45 minutes. Remove the foil and bake an additional 5-10 minutes, or until the top gets nice and golden brown.