What in the world is Croque Madame? I guessed that it was a sandwich you’d have in France, but I wasn’t sure. After a Google search, I learned that it’s tied to a number of recipes. As a sandwich, it’s toasted ham and cheese with a fried egg on top. In England and the U.S., the sandwich features chicken instead of ham, without the fried egg. To put our own spin on it, we in the Test Kitchens turned the flavors of the original Croque Madame sandwich into a hearty egg bake.