On a clean work surface, spread bread out in pairs. On one slice of each pair, spread about 1 tablespoon of mayonnaise. Divide the turkey among the four sandwiches and place on the side spread with mayonnaise. Top the turkey with about 3 tablespoons of stuffing. If desired, top the stuffing with cranberry sauce. Sprinkle cheese over the sandwich fillings, and top with second slice of bread. Press the sandwich tightly together. Brush both sides of the sandwich with melted butter.
Heat Griddler or grill pan over medium heat. Brush plates or pan with melted butter. Place 2 of the sandwiches in the hot pan or Griddler. Close the Griddler or press with grill press and grill 5 to 8 minutes per side or until golden brown and cheese is melted. Repeat process with remaining sandwiches. Serve hot. Makes 4 sandwiches.