Cheesy, Gooey Croques Monsieurs

Ingredients

• 5 1/2 tablespoons unsalted butter, plus more if necessary, divided
• 1 1/2 tablespoons all-purpose flour
• 1 cup milk
• 6 ounces grated Gruyère, Comté, or Swiss cheese, plus more if desired, divided
• Kosher salt and freshly ground black pepper
• 8 slices soft bread, such as brioche or good-quality sandwich bread
• 8 ounces good-quality thinly sliced ham
• 4 teaspoons Dijon mustard

Directions

1. Heat the oven to 350 degrees F. In a small saucepan over medium-high heat, combine 1 1/2 tablespoons butter with the flour and cook until the butter melts and the mixture becomes a paste. Cook for about 1 minute more, stirring, until the flour no longer smells raw. Whisk in the milk until the sauce is smooth, then keep whisking as it reaches a simmer and starts to thicken a bit. Reduce the heat to low and cook, stirring, until the sauce coats the back of a wooden spoon, about 3 minutes. Add 4 ounces cheese and whisk until smooth, sliding the pan on and off the heat as needed so the cheese melts gently without the sauce bubbling hard. Season the Mornay with salt and pepper, and keep it warm.
2. Set a large cast iron skillet over medium heat. In batches, toast each bread slice in the remaining butter until both sides are golden, about 2 minutes per side. Swirl the skillet and turn the bread as needed for even color, adding more butter if the pan starts to look dry.
3. Move the toasted bread to a work surface. Put the ham on half of the slices, then spoon a generous layer of Mornay over the ham. Scatter the remaining grated cheese over the sauce. Spread Dijon mustard on the other bread slices, then close the sandwiches. Cover the top of each sandwich with more Mornay, spreading it all the way to the edges, and add more grated cheese on top if desired.
4. Place the sandwiches on a baking sheet and warm them in the oven until heated through and the cheese has melted. Switch on the broiler, move the pan to the top rack, and broil until the tops are lightly browned, about 2 minutes. Watch closely, since broilers can move fast. Serve right away.