Béchamel: In small saucepan, melt butter over medium heat; add flour and cook, whisking constantly, for 1 minute. Whisk in milk and bring to boil; reduce heat and simmer, whisking, until thickened, about 3 minutes. Stir in nutmeg, salt and pepper. Set aside.
Spread mustard over 4 of the bread slices; top each with 1 slice each Gruyère cheese and ham. Top with remaining bread. Brush butter over outsides of bread.
Heat large ovenproof skillet over medium heat; brush with oil. Cook sandwiches until golden, about 3 minutes per side.
Pour béchamel onto sandwiches, without dripping down sides; sprinkle with shredded Gruyère cheese. Broil until cheese is melted and light golden, 2 to 4 minutes.
Recipe by Family & Friends Recipes at https://recipes.van-ginneken.com/croque-monsieur/