In a medium mixing bowl, combine mashed potatoes and stuffing until combined. Shape them into 4 equal patties.
In a large pan, heat oil or butter on medium heat. Add patties and cook for 5 minutes on one side, then flip and cook on the other side until golden brown and heated through. Add turkey to the pan around the patties and cook until heated through.
Place patties on bread and top with cooked turkey and a slice of cheese.
Add more butter or oil to the pan and heat on medium. Crack eggs into the pan fry until yolks are cooked to desired firmness. Season with salt and pepper. Place eggs on top of cheese.
Top with remaining bread slice and serve.