Heat oven to 400°F. Toast bread on sheets 5 minutes per side until dry and lightly golden.
Melt butter in saucepan over medium. Stir in flour 1 minute; gradually whisk in milk. Simmer 4 minutes until smooth and lightly thickened; add salt, pepper, and nutmeg.
Spread 1/2 cup sauce in 9-by-13-inch dish. Spread toast with mustard; make six sandwiches with ham and 5 ounces Gruyere. Halve; arrange snugly in dish.
Pour remaining sauce over sandwiches; top with remaining Gruyere. Bake 15 to 20 minutes until bubbling and middle filling 165°F.
Broil 1 to 2 minutes, watching constantly, until cheese brown-blistered. Rest 10 minutes; divide into eight portions.