In a medium saucepan set over medium heat, melt 3 tablespoons unsalted butter. Once melted and foaming, add 3 tablespoons all-purpose flour and whisk constantly for 1 to 2 minutes until the mixture is pale, bubbly and smells slightly nutty (do not let it brown).

Add milk and season

Gradually pour in 2 cups whole milk while whisking continuously to avoid lumps. Continue whisking as the sauce thickens, about 4 to 6 minutes, until it coats the back of a spoon and is smooth. Reduce heat to low. Whisk in 1 teaspoon Dijon mustard, 1 teaspoon grated nutmeg, 1 teaspoon kosher salt, and 1 teaspoon freshly ground black pepper. Taste and adjust seasoning. Keep warm over very low heat, stirring occasionally.

Sandwiches

Prepare bread

Preheat the oven to 400°F (200°C). Lightly butter one side of each of the 8 slices of bread with the 4 tablespoons softened unsalted butter. The buttered side will be the exterior of the sandwich to promote browning.

Assemble sandwiches

Place 4 slices of bread buttered-side down on a work surface. On each slice distribute about 1/4 cup of grated Gruyère (from the 2 cups) in an even layer. Top the cheese with two slices of thinly sliced cooked ham. If using, add one thin slice of Emmental or additional Gruyère on top of the ham for extra melt. Spoon about 2 to 3 tablespoons of the warm bechamel sauce over the filling on each sandwich, spreading it slightly but keeping some room at the edges. Finish each sandwich with the remaining 4 slices of bread, buttered-side up.

Optional skillet browning

For an extra-crispy exterior, heat a large skillet over medium heat. Working in batches, place sandwiches buttered-side down in the dry skillet and cook 1 to 2 minutes until golden brown, then flip and brown the other side briefly (30–45 seconds). Transfer to a baking sheet lined with parchment, browned side down.

Topping & Finishing

Top with bechamel and cheese

Place assembled sandwiches on a baking sheet (if you browned them in a skillet, keep the browned side down). Spoon a generous layer—about 2 to 3 tablespoons—of the reserved bechamel sauce over the top of each sandwich, spreading to cover most of the surface. Sprinkle about 2 to 3 tablespoons (roughly 1/4 cup) of extra grated Gruyère on top of each sauced sandwich; use the remaining grated cheese evenly among the 4 sandwiches.

Egg glaze (optional)

In a small bowl, whisk 1 egg yolk with 1 teaspoon whole milk. Lightly brush the exposed edges of the bread with this glaze to encourage deep golden color while baking.

Bake

Bake in the preheated 400°F (200°C) oven for 8 to 12 minutes until the topping is bubbling and the cheese is melted. For a browned crust, switch the oven to broil on high for 1 to 2 minutes—watch closely to prevent burning—until the top is deeply golden and slightly caramelized.

Rest and serve

Remove from the oven and let the Croque Monsieur rest 2 to 3 minutes. Slice each sandwich diagonally and serve immediately while hot and melty.