Step 1: Cheese Sauce ... Add the butter and bay leaf to a pot; and bring to medium heat. Once the butter has melted; add the flour; and whisk until they are combined. Cook just a couple of minutes until the 'raw' flour taste is gone. Then, slowly add the room temperature milk, nutmeg, mustard, salt, and pepper; and, continue to whisk on medium heat, until there are no lumps - and, the sauce has thickened. DO NOT let the sauce come up to a boil; or, it could curdle or separate.
Step 2: Simmer on LOW heat, covered - about 5 minutes minutes before adding the cheese. Once the sauce has simmered; remove from the heat, (remove the bay leaf), and add the cheeses. Stir until everything is creamy and melted. As you prepare the cheese sauce; toast your bread. Just cover the sauce; and, set on a back burner to keep warm, stirring now and then.
Step 3: Bread ... Lightly spread the 8 slices of bread with butter on both sides. Then, bake or 'toast' the bread on a sheet pan, lined with parchment paper or foil; in a 400 degree oven, until golden brown on each side (4-5 minutes). The sandwiches will be baked in the oven; so, just leave the bread right on the pan.
Step 4: Sandwich ... Top each toasted slice of bread with 2 tablespoons of the cheesy bechemel sauce. Then, top 4 of the slices with ham, 1 tablespoon of shredded gruyere cheese on top of the ham; and, the second slice of bread, spread with the bechemel sauce - sauce side down.
Step 5: Finish and Bake ... First, reduce the oven temp to 350 degrees. Then, pour 1/4 cup of the bechemel sauce over each sandwich; and top with 1/4 cup of the gruyere on top of that. Don't worry if it drips down the sides a bit. Then, bake on the middle shelf for 5-7 minutes, until heated through. Then, I like to turn on the broiler the last minute, just to melt and brown up the cheese on top. If the cheese is already melted; the broiler isn't necessary. That just depends on your oven.
Step 6: Eggs ... As the sandwiches bake; cook your eggs. Now a Croque Monsieur doesn't have eggs - A Croque Madame does. Add the butter to a non-stick pan; and, bring to medium heat. Then, crack in the 4 eggs; and, once the whites begin to set - add approximately 1/4 cup water, cover; and cook on medium low heat, until the eggs are set - and, the yolks still runny. I like to slow cook them; so, there are no brown edges. The water allows them to steam rather than brown.
Step 7: Finish ... Top each sandwich with ones of the eggs. And, there is a little sauce leftover over - and; me and my friends, we like to drizzle a little more over the egg. One of my friends adds a little on the side as a dip.
Step 8: Garnish, Serve, and ENJOY! ... Garnish with chives and dig in. A Crispy, Cheesy, Ooey, Gooey 'Ham and Cheese' Sandwich! Serve with a small fresh green salad or fruit salad. Makes a great breakfast, brunch, lunch, or light dinner!
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