Preheat the oven to 350 degrees F.

Cut the rolls in half crosswise and spread the top half of bread with the mayonnaise. Spread the other slices with the mustard and a little of the cranberry sauce. Season with salt and pepper. Divied the cheese betweeen the rolls on top of the mayonnaise. Divide the turkey between the rolls and place on top of the cheese. Place the remaining slices of bread on top of the cheese. In a shallow bowl, whisk the eggs and milk together. Dip each sandwich in the egg mixture.

In a skillet, melt the butter over medium heat. Place the sandwiches in the pan and pan-fry until golden, 1 to 2 minutes per side.

Place the sandwiches on a baking sheet and place in the oven. Cook until the cheese melts. Remove from the oven. Slice in half and serve with any remaining leftover cranberry sauce.