Cook pasta in salted water according to directions on the package. Drain and rinse with cold water. Cool the pasta down and stir in the beaten eggs and 1 teaspoon salt.
Meanwhile, melt the butter in a large skillet. Add the onions and sauté until translucent. Add the ground lamb and cook with the onions until browned, breaking it down to crumble. Stir in the tomato sauce, cinnamon, oregano, cumin, and salt and pepper to taste. Simmer for 5 minutes.
Preheat your oven to 350 degrees F. Spray a deep casserole dish with nonstick spray.
Scoop half of the pasta into the bottom of your prepared dish. Sprinkle with 1 cup of the cheese. Pour the meat mixture to create an even layer and sprinkle with a cup of cheese. Add the remaining pasta on top of the meat and sprinkle with another cup of cheese! Top with the béchamel sauce and sprinkle with the remaining cheese.
Bake 45 minutes, or until the sauce is bubbly and golden on top. Let sit at room temperature for at least 20 minutes before serving (or refrigerate to let the layers set and then warm up later to serve).
Melt the butter in a medium saucepan. Whisk in the flour and then gradually whisk in the hot milk. Cook, whisking constantly until the sauce is smooth and thickened. Stir in the salt, pepper, and nutmeg.
Remove from heat and let cool. When the sauce is lukewarm, whisk in the eggs.
Traditional pastitsio uses Kasseri or Kefalotiri cheese. If you have trouble locating Greek cheese, sub with Romano pecorino, mozzarella, mild cheddar, or provolone.
You can use any tube style pasta such as penne, bucatini, or Misko.