Thinly spread mustard on each slice of bread. Lay thin slices of sausage on two slices of bread, top with apple, then the cheese. Top with the remaining slices to make two sandwiches. Compact each sandwich lightly by pressing on it with your hand.
Melt butter in a heavy skillet over medium heat; , lightly beat eggs and milk together in a wide shallow dish. Dip both sides of each sandwich in egg mixture and place in hot skillet. Cook until cheese is melted, flipping sandwiches once to thoroughly brown each side, about 4 to 5 minutes.
Serve immediately, while the cheese is still gooey!