Preheat the air fryer to 350°F for 3 to 5 minutes. Lightly grease a deep 7-inch round casserole dish.
In a large bowl, stir together the turkey, gravy, and pepper. Taste and add salt only if needed. Spread the mixture into the dish.
Cover the dish tightly with aluminum foil and air fry at 350°F for 12 minutes, until the gravy bubbles at the edges.
Meanwhile, crumble the stuffing into a bowl. If it is dry, stir in broth a tablespoon at a time until it holds together when pressed.
Remove the dish from the air fryer, take off the foil, and stir the turkey mixture. Spoon the stuffing over the top in an even layer and drizzle with the melted butter.
Return the dish to the air fryer, uncovered, and cook at 350°F for 8 to 10 minutes, until the stuffing is crisp and browned and the center reads 165°F.
Rest 5 minutes. Serve with cranberry sauce.