Melt 1/4 cup butter in a small saucepan over medium heat. Gradually stir the flour into the butter. Add small portions of the cream and wine alternately, whisking after each addition to thicken before introducing the next amount. Season with salt, pepper, and nutmeg. Melt the cheese into the liquid in small amounts, stirring continually. Reduce heat to low and keep sauce warm until using.
Place a large skillet over medium-high heat. Spread 1/2 teaspoon of butter on one side of each slice of bread; spread about 1/2 tablespoon of Dijon mustard on the opposite side of each slice. Assemble the sandwiches by placing four slices of bread, buttered side down, into the skillet. Top each slice of bread with two slices of ham folded to completely fit on the bread; spoon equal amounts of the cheese sauce over the ham, reserving some of the sauce for later. Place the remaining slices of bread, mustard side down, atop the ham and cheese. Grill the sandwiches on each side until the bread is an even, golden brown color. Spoon a little of the cheese sauce on top of each sandwich before serving. Garnish each sandwich with 1 teaspoon of parsley.