Pastichio (Greek Lasagna)

1.Melt 1 tablespoon of butter in a large skillet over medium-high heat. Stir in onion and cook until it begins to soften, about 3 minutes. Stir in the ground beef, and cook until crumbly and no longer pink. Pour in the water and tomato paste. Season with salt, pepper, allspice, nutmeg, and cinnamon; cover, and simmer for 5 minutes. Remove from heat, adjust salt to taste, then refrigerate until cold. Once cold, remove any congealed fat, and thoroughly mix with 2 beaten eggs, and set aside. 2.Preheat oven to 400 degrees F (200 degrees C). 3.Bring a large pot of lightly salted water to a boil. Add macaroni and cook for 8 to 10 minutes or until al dente; drain, and rinse under cold water to cool. Mix the macaroni in 2 beaten eggs until well coated. 4.Evenly spread half of the macaroni mixture into a 11x14x2 inch baking pan, sprinkle with 1/2 cup of the grated parmesan cheese, and drizzle with 1/2 cup of melted butter. Spread the meat mixture overtop, then finish with the remaining macaroni. Sprinkle the macaroni with another 1/2 cup of Parmesan cheese, and drizzle with 1/2 cup of melted butter. 5.While pasta is cooking, prepare Bechamel. Melt butter in saucepan over medium heat, using whisk, slowly incorporating flour.Once flour has been incorporated, slowly add hot milk while shitring constantlly to avoid sticking & burning. Once thickened to mashed potato stage, remove from heat, add parmesan eggs, nutmeg and pepper. 6. Layer 1/2 of pasta in 9"x11" pan. Add ground beef mixture and spread evenly. Layer remaining noodles. Spread bechamel sauce evenly on top layer, about 1/2-3/4" thick layer. Cover and bake for 15-20 min. Remove cover and continue baking until golden brown 5-10 min.