Cook and strain spaghetti according to package directions.
Beat eggs in a bowl. Stir in Parmesan cheese and season with salt, pepper and a pinch of nutmeg.
Mix in cooked spaghetti and stir well.
Foam half of the butter in a frying pan and fry the pasta mixture in it, without stirring, over moderate heat until golden.
Melt remaining butter on top of omelet. Turn omelet over and fry the other side until crispy.
Portion and serve hot.