What French dish is a hot sandwich of ham, cheese, and béchamel sauce, often gratinéed?

The French hot sandwich of ham, cheese, and béchamel sauce is a croque-monsieur. It is usually made with slices of pain de mie, cooked ham, and a melting cheese such as Gruyère, then fried or baked until hot and crisp.

The name combines croque, meaning “crunch,” with monsieur, or “mister.” References to the sandwich appear by 1891, when an account described toasted bread, butter, Gruyère, ham, and cayenne pepper being assembled and fried in a pan. Béchamel is a common topping, especially in brasserie-style versions, but it is not required in every traditional preparation.

The most famous variation is the croque-madame, which adds a fried or poached egg on top. That egg is the key distinction; croque-madame is not simply another name for the original sandwich. Other variations may use Comté or Emmental, or add tomato, smoked salmon, or different cheeses.