Toast all the bread at medium heat (2-3 mins each side) in the large sauce pan (or bake the bread pieces in the oven for 3-5 mins).
Melt the butter at low heat in the small saucepan.
Add the flour to the molten butter and stir with a wooden spoon constantly for about 2-3 mins.
Add the milk into the butter/flour mixture. Keep the heat at low and whisk constantly until the sauce (béchamel) thickens.
Take the sauce off heat and season with nutmeg (and salt).
Spread the toasted bread with the butter/milk sauce with a spoon. Sprinkle grated gruyere cheese on top of the sauce.
Place 2-3 pieces of ham on half of the bread pieces. (Each bread has 2-3 pieces of ham).
Top the above bread pieces with the other half of bread slices. (cheese is in the middle)
Slather the tops with the sauce and sprinkle with the remaining gruyere cheese.
Bake the sandwiches for 8-10 minutes.
Turn on broiler to low heat (400F) and broil for 3 to 5 mins, or until the topping is bubbly and lightly browned.
Serve hot.
Video
Notes
-Since cheese and ham are sort of salty, you don't have to add salt to the butter/flour/milk sauce, which is called béchamel in French. -You don't have to add nutmeg to the sauce either. -Some recipes use country bread. The bread I used was bought at a local Japanese bakery. As long as you don't use sourdough or whole wheat, I think you are fine.
Keyword béchamel, croque madame, Croque Monsieur, french ham, Gruyere cheese, ham, white sauce, 三明治, 法式三明治, 法餐