Preheat oven to 400 degrees. Line a baking sheet with a nonstick baking mat; brush with butter.
In a 9-by-13-inch baking dish, whisk together eggs and milk. Season with salt and pepper.
Spread cranberry sauce on 4 slices of bread. Top with turkey; season with salt and pepper.
Sprinkle cheese evenly over turkey. Top with remaining bread slices.
Carefully transfer sandwiches to egg mixture and soak, pressing lightly with a spatula, 1 minute a side.
Transfer to baking sheet; bake 15 minutes. Flip and bake 7 minutes more.
Let rest 5 minutes before serving.
