Make the herbs de provence: Combine all ingredients in an airtight container and store in a cool, dark place for up to 3 months.
Make the béchamel: Melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 2 minutes, whisking occasionally, until the roux smells nutty. Whisk in the milk, thyme, salt, pepper, and nutmeg. Cook the milk mixture, whisking to smooth, until thickened. Add in the salt, pepper, and nutmeg to taste. Set the sauce aside to cool and thicken slightly while preparing the sandwiches.
Assemble the sandwiches: Heat the broiler to high and move the top rack within 6 inches of the broiler. Line a half-sheet pan with aluminum foil, coat with nonstick spray, and set two bread slices on the pan. Spread the mustard onto two of the bread slices — these will be the bottoms of the sandwiches.
Top the two bottom slices with 2 ounces each of the ham. Cover each of the sandwiches with about 1 once of the Gruyere. Broil these open-faced sandwiches until the cheese is melted, 2 to 3 minutes.
Top the broiled sandwiches with another slice of bread, cover the sandwiches with the béchamel and top with the remaining Gruyere. Sprinkle each sandwich with 1/2 teaspoon of the herbs de provence mixture and broil again until the cheese is golden brown, 4 to 5 minutes. Cool for 5 minutes before serving or you'll burn your face off.
Serve with a knife and fork and plenty of napkins.