Take a trip to Paris, France in your kitchen. A French dish basically topping a Ham and Cheese Sandwich with an egg but this adds a great Bechamel Sauce (How they do it in France). This is such a yummy dish, you can eat it for Breakfast, Lunch or Dinner!
Preheat the oven to 400 degrees F. Grease an 8-inch square baking dish.
Toss Gruyere and Emmentaler cheese together. (You can also find this mixture already preshredded as Fondue Mixture, if not grate seperately) If you'd like you can use just 2 cups of Gruyere cheese. I like both.
Melt 6 tablespoons of butter in a large skillet over low heat until bubbling. Whisk in the flour and cook for 1 minute. Slowly whisk in the milk and cook until thick and bubbling, 3 to 5 minutes more. Whisk in the mustard, salt, pepper, and nutmeg.
Pour a thin layer of the sauce into the prepared baking dish and cover it with 5 or 6 slices of the bread, then slices of the ham and an even layer of the Gruyere/Emmentaler Cheese Mixture. Repeat the layers once more, ending with a third layer of sauce to cover all. Bake the casserole for 30 minutes. Remove it from the oven and cut into 6 equal pieces.
Working in 2 batches, melt 1 tablespoon of butter in a large skillet over medium-high heat. Crack 3 eggs into the skillet and season with salt and pepper, to taste. Cook until the whites are nearly set, about 3 minutes. Carefully flip the eggs and continue cooking until the whites are completely set, about 1 minute more. You're going to top each portion of the casserole with a fried egg. Repeat with the remaining 3 eggs and 1 tablespoon butter. Top with Gruyere/Emmentaler Cheese Mixture and it in the oven for a few minutes until cheese melts.
Serve with Fresh Fruit or a light Field Green Salad on the side.