Croque Madame

Directions

• Set the oven’s broiler to high and place a rack about 6 inches from the heat source.
• 1/2 tablespoons of butter should be melted in a pot over low heat. Add the flour and whisk until just beginning to brown, about 3 minutes. Add milk and constantly stir as you come to a boil. Once boiling, immediately reduce heat, and then simmer for five minutes. Add half of the Gruyère cheese, salt, pepper, and nutmeg; cook for about two minutes, or until cheese is melted. Turn off the heat and leave the pot alone.
• On two pieces of bread, spread roughly 1 teaspoon of butter. Layer each with a ham slice and a spoonful of cheesy sauce. The remaining 2 pieces of bread should be coated with 1 teaspoon butter, followed by a layer of Dijon mustard, then the remaining Gruyère. Place a baking sheet with all 4 pieces on it.
• In the preheated oven, broil for 2 to 3 minutes, or until the cheese is practically melted. Take the toast out of the oven, assemble it into 2 sandwiches, and top each with the remaining cheese sauce. Return to the broiler for another 2 minutes or until the sauce begins to brown.
• Remaining butter should be heated in a nonstick skillet over medium-high heat while the sandwiches are broiling. Two eggs should be cracked into the skillet with complete separation between them. Add salt and pepper to taste. When the whites are set but the yolks are still runny, add water, cover, and baste for about 2 minutes.
• Each sandwich should have an egg on top and, if desired, dill. Serve right away.