In a small bowl, mix together the mayo and dijon mustard. Set aside.
Preheat a griddle pan over medium heat. Butter one side of 4 slices of bread. Place the slices, butter side down, onto the hot pan. Place a slice of cheese, a slice of prosciutto, 1/2 cup of chicken, 2 slices of prosciutto, and a slice of cheese in that order on each slice of bread. Take the four remaining slices of bread and spread 1 tablespoon of the mayo/mustard mixture on one side and butter the other side. Place the slices, mayo side down and butter side up on the sandwiches. Cook for 3-4 minutes on each side or until brown and the cheese is melted. Remove from heat.
Serve the chicken cordon bleu grilled cheese sandwiches immediately with your favorite tomato soup recipe and enjoy!
I like to use a store-bought rotisserie chicken for this recipe. Just pull the chicken off the bone and refrigerate until you are ready to use!