There are so many variations on the classic Croque Monsieur, which contains cheese (typically Emmental) and ham. Usually you would find melted cheese over the sandwich too. If fried egg is thrown on top they call it a Croque Madame. The difference with a Monte Cristo, is that instead of being fried in butter with cheese melted over it, it’s soaked in egg wash and fried (similar to French Toast).
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