Slice the eggs in half. Shred the smoked salmon into smaller bits. Add both to a small baking dish. Sprinkle with half of the chopped parsley. Season with pepper and salt.

Add the unsalted butter to a large saucepan. Season with pepper, salt and nutmeg . Place this over medium-high heat for 2 minutes. Then add the flour to the melted butter.

Stir the flour and butter well. Let this mixture bake for another minute.

Stir in half of the grated cheese. Gradually pour in the milk.

Keep stirring the white sauce until it starts to thicken. Then take the sauce off the heat. Stir in the rest of the chopped parsley. Ladle the sauce on top of the eggs and smoked salmon in the baking dish.

Sprinkle with the rest of the grated cheese. Grill the eggs for 6 to 8 minutes. The top should be browned nicely. Then remove the dish from the grill. Let it cool for 2 minutes. Divide the eggs and salmon over plates. Serve warm.