Make the bechamel. In a small saucepot, heat the milk over medium heat until warm to the touch; set aside. In a separate small saucepot, melt the butter over medium heat. Add the flour, reduce the heat to low and cook, whisking continuously, until the raw flour taste has been cooked out, about 2 minutes. Whisk in the warm milk until smooth. Grate the nutmeg into the bechamel.
Season the bechamel with salt and bring to a simmer, whisking continuously, until thickened, about 2 minutes. Remove from the heat and add the Gruyere. Whisk the mixture until smooth and set aside.
Assemble the sandwiches. Heat the broiler on high. Set the bread on a sheet pan and place 3 slices of the ham on each slice of bread. Spoon a thin layer of the bechamel on top of the ham. Divide the Gruyere evenly among the sandwiches and season with pepper. Broil until the cheese melts and turns golden brown, about 3 minutes.