In a small bowl mix together the mayo and mustard; aside.
In a shallow wide bowl whisk together the eggs and milk – big enough to dip one side of the sandwich in.
Lay out three pieces of bread, spread a thin layer of the mayo on one piece and top with a slice of cheese and then a slice of turkey (I used several slices because I used thinly sliced). For the second piece of bread spread on a little more of the mayo mixture and top with another slice of turkey and place another slice of cheese on top and place the 3rd piece of bread on top of that to form the sandwich.(do not skip the last slice of cheese it is needed to hold the sandwich together when the cheese melts).
In a nonstick skillet over medium high heat melt the butter along with the oil. Dip each side of the sandwich in the egg mixture like you are making french toast. Place in the skillet and cook until golden brown, flip, and continue cooking until nicely browned and cheese is melted.