Featured on menus in Paris as early as 1910 as a “gentlemans sandwich” – a classic french recipe
Preheat oven to 400.
Melt butter on low heat in small saucepan. At flour and whisk until incorporated, about 2 minutes. Slowly add hot milk to mixture, whisking until blended well and no lumps and has thickened. Take off heat, add salt and pepper, 1/2 cup of Gruyère and all the Parmesan. Mix until blended. Set aside.
Place slices of bread on parchment lined baking sheet and toast lightly, about 5 minutes. Turn each slice and bake another 2 minutes. Brush slices of bread with mustard and add slice of ham to half the toasted slices. Sprinkle with 1/2 of remaining Gruyère. Top with the toasted bread slice. Slather the top with cheese sauce and remaining Gruyère and bake for 5 minutes. Turn broiler on and broil for about 3 minutes.
Optional: while sandwiches are broiling you can fry eggs in pan and place on top of each sandwich.