Croque-madame: ham, Gruyère, béchamel and fried egg
A croque-madame starts from the same hot ham-and-cheese sandwich family as a croque-monsieur, but the visible egg on top is not a garnish that can be omitted without changing the dish. This bistro build uses pain de mie, cooked ham, Gruyère, Dijon mustard and béchamel, then finishes each sandwich with one fried egg. The egg makes the plate richer and creates the clear identity boundary from the simpler croque-monsieur that follows in this pair of recipes.
Béchamel is used in a controlled amount rather than as a blanket of loose sauce. Cook the butter and flour gently, whisk in cold milk and stop when the sauce clings to a spoon. Exactly 60 g goes on each sandwich, enough to carry the cheese into a gratinated top while leaving the bottom bread crisp. The oven should deliver bubbling sauce, melted cheese and browned edges in the same short window.
The egg needs an explicit safety choice. Here the yolk is deliberately left soft, so the recipe requires pasteurized shell eggs. Fry until the whites are fully opaque and set, then place one egg on each croque and serve immediately. Ordinary unpasteurized eggs should instead be cooked until both white and yolk are firm; a vague choice between runny and fully cooked eggs would not be safe enough for an executable recipe.
