Bring a large pot of lightly salted water to a boil. Add ziti and cook for 8 to 10 minutes or until al dente; drain and return to pan.
Melt butter until golden brown and pour over ziti, add 1/4 cup of the Parmesan cheese, nutmeg, salt, pepper and toss well; allow to cool. Add eggs and toss again; set aside.
To make meat sauce: Gently fry onion and garlic in butter in a skillet until onion is soft. Increase heat and add ground beef; stir well. Cook until meat begins to brown. Add tomato paste, wine, broth, parsley, salt and pepper. Cover and simmer over low heat for 20 minutes.
To make cream sauce: Melt butter in saucepan, stir in flour and cook gently for 2 minutes. Pour in milk all at once and bring to a boil, stirring constantly. Boil gently for 1 minute. Add nutmeg, salt, pepper and cool slightly before stirring in beaten egg. Transfer 1/2 cup of this sauce to the meat sauce.
To assemble pastitsio: Grease a 9x13 inch baking dish. Spoon half of the prepared ziti evenly in the bottom and top with meat sauce. Top that with remaining ziti. Pour on cream sauce and spread to completely cover ziti. Sprinkle remaining cheese on top.
Bake in a preheated oven for 50 minutes or until golden brown. Let stand 10 minutes before cutting into squares to serve.