Dice and chop onion, carrot, celery and garlic in food processor. To make the meat sauce, heat the butter in a frying pan and add the chopped vegetables, garlic and pancetta. Cook over medium heat for 4 to 5 minutes or until soft and lightly golden. Add the ground beef and increase the heat a little and cook for 8 minutes or until colored but not brown, stirring to break up the lumps. Add the oregano and nutmeg and season well.

Stir in the chicken livers, and cook until they change color. Pour in the vermouth, increase the heat and cook until it has evaporated. Add the beef stock and tomato paste and simmer for 1 hour, but towards the end of cooking allow all the liquid to be absorbed. Stir in the cream, remove from heat and allow to cool for 15 minutes. Stir in the eggs.

Stir the cream into the hot Béchamel, preheat the oven to 400°F and grease a 9 x 6 x 3 inch flameproof dish.
If you are using fresh pasta, cut it into manageable sheets and cook in batches in a large saucepan of boiling salted water until al dente. Scoop out each batch with a slotted spoon as it is done and drop into a bowl of cold water. Spread the sheets out in a single layer on a kitchen towel, turning them over once to blot dry each side. Trim away any torn edges.

Spread half the meat sauce in the dish, and then cover with a slightly overlapping layer of pasta sheets. Spread half the Béchamel sauce over this and sprinkle with half the Parmesan. Repeat the layers, finishing with a layer of Béchamel sauce, Parmesan and mozzarella.

Bake for 40 minutes until golden brown, and let rest for 15 minutes before serving.