Croque-Monsieur et Croque-Madame
5 tablespoons unsalted butter
2 1/2 tablespoons all-purpose flour
1 3/4 cups milk (whole or 2%)
2 teaspoons Worcestershire sauce
1 teaspoon fresh thyme or 1/4 teaspoon dried thyme
1/4 teaspoon grated nutmeg
salt and pepper
8 slices country-style white sandwich bread
4 teaspoons Dijon mustard
4 ounces Gruyere Cheese
12 ounces sliced ham
1/2 cup Parmigiano-Reggiano, finely grated
4 eggs, optional
For the sauce:
In a medium saucepan over medium-low heat melt 2 tablespoons of the butter. Whisk in the flour and continue whisking just until it turns beige, about 20 seconds. Whisk in the milk in a slow, steady stream; continue whisking until smooth,thickened and slightly bubbling, 2 to 3 minutes. Whisk in the Worcestershire sauce, thyme, nutmeg, 1/4 teaspoon salt and pepper. Remove from heat and set aside. Whisking occasionally to prevent a skin from forming.
For the sandwich:
Spread four of the bread slices with 1 teaspoon of Dijon. Layer the Gruyere and ham on the bread in this pattern: cheese, ham, cheese. Top with the remaining bread.
Melt 1 tablespoon of the butter on a griddle or a 12-inch skillet. Cook the sandwiches until brown and crisp, turning once halfway through the cooking, about 4 minutes, Transfer to a rimmed baking sheet. Repeat with remaining sandwiches.
Ladle the bechamel sauce over the sandwiches, letting it run down the sides. Sprinkle with the Parmigiano-Reggiano cheese. Place under a preheated broiler for 3-4 minutes or until the sauce is bubbling and the top is beginning to brown. Remove from the boiler and with a spatula transfer to a serving plate.
Heat a 10-inch skillet, melt the remaining butter over medium heat. Crack the eggs into the skillet and fry them sunny side up until the whites are set but the yolks are still runny, 3-4 minutes. Sprinkle with salt and pepper. Remove from skillet and place on the egg.