Cook the macaroni in a large pot of salted water for 10 minutes or until al-dente. Drain and return to the pan.
Melt the butter in a small saucepan until golden in color, then pour it over the macaroni. Add the Nutmeg and half the cheese and season to taste with salt and pepper. Let cool and then stir in the egg. Set aside.
In a large frying pan, heat the olive oil then add the onion and garlic. Cook over medium heat for 5 minutes or until the onion is soft. Increase the heat and add the ground beef. Stir for 5 minutes or until the meat is browned.
Add the wine and cook over high heat for 1 minute, or until the wine has nearly evaporated. Add the stock, tomato paste, oregano, salt and pepper. Reduce the heat and simmer, covered, for 15-20 minutes.
Preheat the oven to 350F, and lightly grease a 1.5 liter baking dish.
While the meat simmers, make the béchamel sauce by melting the butter in a small saucepan over low heat. Stir in the flour and cook for 1 minute until pale and foaming. Remove from heat and gradually stir in the milk. Return to the flame and whisk constantly until the sauce comes to a boil and thickens. Reduce the heat and simmer for 2 minutes. Add the nutmeg and season with salt and pepper. Allow the sauce to cool a little bit and then temper the beaten eggs with a bit of the sauce. Stir the eggs into the sauce.
Add about four tablespoons of the béchamel sauce to the meat sauce and stir to combine.
Spread half the meat sauce in the prepared baking dish. Follow with 1/2 the pasta. Repeat the layers. With the back of a spatula, press the pasta down firmly to pack.
Spread the béchamel sauce over the pasta and sprinkle the remaining cheese on top. Bake for 45 minutes or until the top is golden. Let it stand for at least 15 minutes before serving.