Preheat oven to 350 degrees F.
Cut rolled sausage into patties and slowly fry in a nonstick skillet. Drain and let cool on paper towels. Using the same skillet, drain sausage fat, saving 2 tablespoons on the side.
Finely mince celery and onion and light fry in skillet with 2 tablespoons butter until all pieces are soft.
In a large mixing bowl, add stuffing mix, thyme, pepper, celery salt and sage.
Pour celery and onion mixture over and 2 tablespoons sausage fat over stuffing mix and let cool completely.
Finely crumble cooled sausage mix over mixture.
Add egg. Slowly start adding milk and mix by hand to blend. Keep adding milk and blending mixture until it is almost the consistency of meat loaf.
Place mixture in a casserole pan (9"x13") sprayed with cooking spray and cover with aluminum foil.
Bake for 20 minutes, remove foil and bake for 10 more minutes. Stuffing is done when top is brown.