Heat the oven to 400°F and toast the bread on sheet pans for 5 minutes per side, until dry and lightly golden.
Melt the butter in a saucepan over medium heat. Stir in the flour for 1 minute, then gradually whisk in the milk; simmer for 4 minutes until smooth and lightly thickened. Season with salt, pepper and nutmeg.
Spread 1/2 cup sauce in a 9-by-13-inch dish. Spread the toast with mustard and use the ham and 5 ounces Gruyere to make six sandwiches; halve them and arrange snugly in the dish.
Pour the remaining sauce over the sandwiches and scatter the remaining Gruyere on top. Bake for 15 to 20 minutes, until bubbling and the middle filling reaches 165°F.
Broil for 1 to 2 minutes, watching constantly, until the cheese blisters brown. Rest for 10 minutes and divide the pan into eight portions.