Preheat your oven to 350°F (175°C).
In a large skillet over medium heat, sauté the diced onion and celery until soft, about 5 minutes.
In a large mixing bowl, combine the cooked turkey, sautéed onions and celery, cream of mushroom soup, chicken broth, and thyme. Mix well.
Fold in the stuffing mix until evenly incorporated.
Transfer the mixture to a greased 9x13-inch baking dish.
Sprinkle the shredded cheddar cheese evenly over the casserole.
Cover with aluminum foil and bake for 25 minutes. Remove the foil and bake for an additional 10-15 minutes, or until the cheese is bubbly and golden.
Let the casserole cool for 5-10 minutes before serving.