The croque madame, the classic French ham and cheese sandwich covered in cheesy bechamel, with a fried egg placed on top of it. Ham and cheese never tasted so good!
3 tablespoons unsalted butter
3 tablespoons all purpose flour
2 cups whole milk
12 ounces Gruyère, grated
1/2 cup finely grated Parmesan cheese
Kosher salt, to taste
Freshly ground black pepper, to taste
Freshly grated nutmeg, to taste
Twelve 3/4 inch-thick slices pain de mie or Pullman bread, toasted
6 tablespoons Dijon mustard
12 slices baked ham, thinly sliced
2 tablespoons canola oil
Heat butter in a 2-quart saucepan over medium-high heat. Add flour and cook, whisking, until smooth, about 1 minute. Whisk in milk, and bring to a boil; reduce heat to medium-low and let simmer until slightly reduced and thickened, 6–8 minutes. Add ½ cup grated Gruyère and the Parmesan, and whisk until smooth. Season with salt, pepper, and nutmeg.
Heat broiler to high. Place 6 slices bread on a parchment paper-lined baking sheet, and spread 1 tablespoon mustard over each. Top with 2 slices ham and remaining Gruyère. Broil until cheese begins to melt, 1–2 minutes. Top with remaining bread slices, then pour a generous amount of béchamel on top of each sandwich. Broil until cheese sauce is bubbling and evenly browned, about 3–4 minutes.
Meanwhile, heat oil in a 12-inch cast iron skillet over medium heat. Add eggs, season with salt and pepper, and cook until whites are cooked but yolks are still runny, about 3 minutes. Place an egg on top of each sandwich, and serve hot.
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