Preheat oven to 350 degrees F (175 degrees C).
Heat butter in an oven-proof skillet over medium heat; cook and stir celery and onion in the hot butter until onion is softened, about 10 minutes. Add bread cubes and chicken broth; stir to combine.
Mix gravy and turkey together in a bowl; spoon over stuffing mixture. Layer corn atop turkey gravy. Spread mashed potatoes over corn layer.
Bake casserole in the preheated oven until heated through, 20 minutes. Sprinkle with Cheddar cheese; return to oven. Bake until cheese is melted, about 10 minutes.