1. Make the sauce: In a large saucepan, melt the butter. As soon as it begins to bubble, add the flour and stir vigorously for five minutes over medium heat, until the flour begins to turn golden. Gradually add hot milk, stirring all the while, until smooth. Beat the eggs separately until frothy. Slowly add two ladle fulls of the sauce to the eggs, beating all the while, then return the contents of the bowl back to the saucepan. Cook sauce, stirring, over low heat until thick. Cover with a cloth and set aside.
2. Make the filling: Heat the olive oil and saute the onion and garlic until lightly browned. Add the meat and brown. Spoon off any fat and discard. Add herbs, tomatoes, and wine and let the sauce simmer, uncovered, for 20 minutes. Season with salt, pepper and nutmeg.
3. Boil the pasta until it is al dente. Drain and rinse under cold water. In a large bowl, combine the pasta with 1/2 cup grated cheese, the melted butter, 2 cups of the bechamel sauce and the meat filling. Toss well.
4. Preheat oven to 350 F. Lightly oil a 10" x 15" x 3" baking pan. Spread the pasta evenly in the pan. Pour the bechamel evenly over the top and sprinkle with grated cheese. Bake the pastitsio for at least 1 hour, or until the top is golden and puffed. Remove and cool for 20 minutes before serving.