Add a tablespoon of oil to a large griddle or pan over medium heat.
When the oil starts shimmering, place some stuffing in the oil and toss it around, breaking it into smaller pieces if needed.
Cook the stuffing for 3 to 4 minutes or until it starts to crisp up on the sides. Add turkey, using a spatula to break it up, and mix it in with the stuffing. Cook everything for 3 to 4 more minutes allowing the turkey to warm and brown a little.
Using your spatula, form the pile of stuffing and turkey into a shape similar to the size of your sub roll. Top the pile of stuffing and turkey with sliced cheese while still in the pan or griddle. Cook for 2 more minutes with the cheese on top.
Slice your roll if needed and open it up like a book. Add any mayonnaise if desired. Place the open roll, inside down, on top of the cheese, turkey, and stuffing mixture. Cook everything for another 1 minute with the roll on top to soften the bread.
Using a spatula with your dominant hand, scoop under the turkey, cheese, and stuffing mixture. Using your other hand to hold the top of the bread, flip everything out of the pan while keeping the turkey, and stuffing mixture inside of the roll. Scoop up any mixture that you might have left on the griddle/pan and add to the sandwich.
Add a slathering of cranberry sauce onto the rest of the sandwich and serve.