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1
Melt the butter in a small saucepan over medium heat until just starting to bubble.
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2
Add the flour, and cook, whisking constantly, until smooth but not browned, about 3 minutes.
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3
Whisking constantly, slowly add the milk; continue cooking while whisking until mixture has thickened, about 3 minutes more.
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4
Remove from heat, and add salt, nutmeg, cayenne, and black pepper.
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5
Transfer to a bowl; place plastic wrap directly on surface of sauce, and set aside.
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6
Heat the broiler.
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7
Heat a griddle or large cast-iron skillet over medium-low heat.
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8
Smear one side of bread slices with mustard.
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9
Top 4 slices with a layer each of ham and cheese; cover with the remaining 4 bread slices, pressing gently to adhere.
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10
Generously butter the outer sides, spreading all the way to the edges.
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11
Place the sandwiches on the griddle or in the skillet.
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12
Cook until the bread is golden brown and cheese has melted, 3 to 4 minutes a side.
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13
Transfer to a work surface; divide bechamel sauce evenly over tops, spreading to edges; sprinkle with grated cheese.
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14
Transfer to the broiler, and cook until the cheese topping is melted and golden, 2 to 3 minutes.
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15
Serve immediately.
