Croque Monsieur is essentially a toasted cheese and ham sandwich. Put a fried egg on top and you've got a Croque Madame (the egg is supposed to resemble a lady's hat). What makes the difference between a toasted cheese and ham sandwich and a Croque Monsieur is the cheese – in a Croque Monsieur it comes in the form of a creamy cheese sauce. And boy, does this make a difference!
This is a perfect post-Thanksgiving dish when you have left over turkey and ham.