Butter a shallow 1 1/2-quart casserole. Cover bottom evenly with turkey. Drizzle 3/4 cup gravy (hot or cold, stirred to soften) over the meat. Stir potatoes to soften, mound onto turkey, and swirl to cover surface of meat. Drizzle remaining 1/4 cup gravy over potatoes, then sprinkle evenly with cheese.
Bake in a 450° oven until turkey and potatoes are hot in the center (about 140°), 10 to 15 minutes. If desired, broil 4 to 6 inches from heat until cheese is lightly browned, 2 to 3 minutes. Season portions with salt and pepper to taste.