Croque-Madame recipe is a take on the classic French ham and cheese sandwich (croque-monsieur), topped with ooey gooey cheese and a poached or fried egg. This is the perfect sandwich for any time of the day!
Start making a roux by melting 2 tablespoons of butter in a small saucepan over medium-low heat. Whisk in 2 tablespoons of flour and cook for about 2 minutes.
Slowly add the milk, whisking constantly for another 2 minutes. Reduce heat to low and simmer for about 5 minutes, whisking occasionally, until mixture thickens.
Stir ½ cup of the cheese and the Dijon mustard into the sauce. Season to taste with the salt, pepper. Remove the sauce from the heat and set aside.
Assemble the sandwiches:
Spread 1-2 tablespoons of the Mornay sauce on one side of each piece of bread, layer with the ham and remaining cheese and place together to form the sandwich.
Spread remaining butter on the outside of the bread slices and place buttered side down in a skillet over medium-low heat. Cook until both sides are golden brown and cheese is melted inside.
Transfer sandwiches to a baking sheet. Set skillet aside to cook the eggs later.
Preheat the oven broiler. Divide the remaining Mornay sauce over the top of each sandwich and broil until the tops are browned and bubbling.
While the sandwiches are broiling, lightly fry the eggs sunny-side up over medium heat in the skillet. Remove the sandwiches from the broiler and top each one with an egg.