In a large saucepan, saute onions in butter until opaque. Crumble beef into saucepan and brown.well. Drain off the fat.
Add salt, pepper, tomato sauce, water and sugar. Stir well and simmer 35-40 minutes. At this point there should be very little water in the sauce.
Remove from heat and cool. The meat sauce can be made ahead of time.
In a saucepan, melt butter and then add in the flour, stiring constantly using a wire whisk. Gradually add the warm milk, stirring vigorously until sauce thickens. Add nutmeg, remove from heat and cool.
When ready to use meat sauce, add half of the bread crumbs and 1 1/4 cups parmesan cheese. Stir well and set aside. Preheat oven to 350 degrees F.
Cook the macaroni per package directions in boiling salted water until almost al dente. Drain well, stir in the olive oil and set aside.
Butter an 11x17 inch baking pan and sprinkle with 2 tbsp bread crumbs. Spread half of the macaroni across the baking pan and sprinkle 1/2 cup cheese over top.
Beat the eggs in a bowl using a wire whisk and add in 1/2 cup of the cooled bechamel sauce. Stir well and then add egg mixture into the rest of the bechamel sauce. Add the cheese and stir well.
Cover macaroni layer with meat sauce. Pour half of the bechamel sauce over the meat and cover with remaining macaroni. Sprinkle 1/2 cup cheese over macaroni layer.
Top macaroni layer with remaining bechamel sauce and top with remaining bread crumbs and cheese.
Cook in the oven on a center rack for 50 minutes or until golden brown. Let sit 20 minutes to firm up before cutting and serving.
This casserole freezes well and is easy to reheat. Place the frozen pastitsio, covered loosely with foil, in a 350 degree oven for 1 1/2 hours to 2 hours or until heated through.