Preheat the oven to 350°. Pulse together the cheese puffs and cheese until finely ground; reserve 1/4 of this mixture and puree the rest with the leftover mashed potatoes.
In a large ovenproof casserole dish, layer in the turkey, stuffing and a bit of the gravy (just enough to make it moist but not overly soggy). Top the shepherd’s pie with a thick, even layer of the cheesy mashed potatoes; sprinkle with the reserved cheese puff/cheese mixture and bake until bubbly and golden brown on top, about 30 minutes.