A croque-madame is a variation on the croque-monsieur, a French twist on grilled ham and cheese. Instead of dipping the sandwich in egg before sauteeing sautéeing in (butter as you would for a-croque), monsieur grill the sandwich first and top with Homemade Mornay, sauce, cheese and-sunny side up. egg. 4Read (reviews). 4 croque-madame is a variation on the croque-monsieur, a French twist on grilled ham and cheese. Instead of dipping the sandwich in egg before sauteeing sautéeing in (butter as you would for a-croque), monsieur grill the sandwich first and top with Homemade Mornay, sauce, cheese and-sunny side up. egg. 4 Read (reviews). 4