Croque-Madame

Gather the ingredients.

Melt 1 tablespoon of butter in a medium saucepan over medium heat. Add flour to the butter and cook for 2 minutes, stirring constantly.

Add the milk, 1/4 teaspoon salt, and a dash of nutmeg and cook, stirring, for 3 to 4 minutes, until thickened.

Stir in the Parmesan cheese and half of the Gruyère cheese.

Arrange two slices of bread on a baking sheet and spread with Dijon mustard, if desired. Divide the ham on top of the two slices of bread.

Spread a bit of the thick cheese sauce over the ham, top with the remaining Gruyere and another slice of bread.

Melt 4 tablespoons of butter in a large nonstick skillet over medium heat. Brush the tops of the sandwiches with some of the melted butter.

Place the sandwiches in the hot skillet, buttered side down and brush more butter over the tops. Cook for 2 to 4 minutes on each side until golden brown.

Remove the sandwiches to the baking sheet and spread the remaining cheese sauce over the tops. Be sure to coat the edges to prevent the bread from burning.

Position a rack in the top third of the oven. Turn the oven to broil. Melt the remaining 2 tablespoons of butter in a nonstick skillet over medium heat. Crack each egg into a ramekin then add them slowly to the skillet.

Cover the skillet with a lid and cook for 2 to 3 minutes, or until the whites are set and the yolks are still runny. While the eggs are cooking, place the sandwiches under the broiler and cook for about 2 minutes, or until the sauce is bubbling and beginning to brown.

Remove the sandwiches to plates and top each with a fried egg. Sprinkle with salt and freshly ground black pepper to taste, and serve immediately.