For the béchamel, melt half the butter in a small pan. Add the flour and stir over a medium heat until blended.
Gradually add the milk, whisking continuously into a smooth sauce, then simmer gently for 2 to 3 minutes, or until the sauce has thickened.
Add the mustard, nutmeg and sea salt and black pepper to taste. Set aside.
Preheat the grill to high. Lightly toast the bread on both sides under the grill.
Arrange slices of ham and cheese on each, then top with béchamel sauce. Place back under the grill to brown the béchamel and melt the cheese.
Meanwhile, melt the remaining butter in a frying pan over a low heat. Crack in the egg and fry till the white is cooked but the yolk is still soft, or to your taste. Place the toasts on a plate and top with the egg.