Spread four slices of bread with mustard. Top each slice with 1/4 cup cheese. Divide smoked meat among slices and sprinkle each with 1/4 cup remaining cheese. Top with remaining bread slices. Butter both sides of each sandwich.
Set a large skillet over medium heat. Working in two batches, cook sandwiches until golden and crisp, about six minutes per side. Transfer sandwiches to small baking sheet.
Spoon 1/4 cup Mornay sauce over each sandwich. Broil until brown, about two minutes.
Top each sandwich with a sunny-side-up fried egg and serve immediately.
For the mornay sauce:
In a medium saucepan over medium heat, melt butter. Sprinkle in flour and cook for three minutes, stirring constantly.
Whisk in milk and cream. Cook, stirring frequently, until sauce is thick enough to coat the back of a spoon, about seven minutes. Remove pan from heat and stir in cheese and nutmeg. Season to taste with salt and pepper and keep warm until ready with use.