Prepare the baking dish and soak the pasta: Place a 9x13-inch (3‑quart) baking dish on the counter and add the bucatini or penne. Cover with very hot tap water, add 1 teaspoon salt, stir so the pasta doesn't stick, and let soak 30–40 minutes while you make the sauces.
Preheat the oven to 350°F (175°C) and chop the onion and mince the garlic.
Make the meat sauce: In a large (about 6‑quart) pot over medium heat, melt 2 tablespoons butter. Add the chopped onion and minced garlic and sauté 3–5 minutes until softened. Add the ground beef, cinnamon, nutmeg, and 1 teaspoon salt; break the meat into small pieces and cook until browned and cooked through.
Stir in the 30 ounces of tomato sauce, reduce heat to a simmer, and cook 15 minutes, stirring occasionally. Season with salt and pepper to taste, then remove from heat.
Make the bechamel: In a separate pot over medium heat, melt 1/2 cup butter, then whisk in 1/2 cup flour to form a roux. Cook 1–2 minutes without browning, then gradually whisk in 4 cups milk until smooth.
Bring the bechamel to a gentle simmer, stirring until it thickens to a gravy-like consistency. Remove from heat, then vigorously whisk in the 2 reserved egg yolks until fully incorporated. Stir in 1 cup shredded Italian cheese and 1 teaspoon salt and 1/8 teaspoon nutmeg until the cheese melts and the sauce is smooth.
Drain the soaking pasta, leaving a little water in the dish if desired. Toss the pasta with the 2 reserved egg whites and the 6 ounces crumbled feta until evenly combined, then spread in an even layer in the prepared baking dish. Sprinkle 2 cups shredded Italian blend cheese evenly over the pasta layer.
Spread the meat sauce evenly over the cheese layer, then gently spoon the bechamel over the meat to cover it. Finish by sprinkling the remaining 1 cup shredded Italian blend cheese over the top.
Bake: Place the 9x13 dish on a rimmed baking sheet if not using a deep-dish pan. Bake uncovered on the lower oven rack at 350°F for 30–40 minutes until the top is golden brown; cover loosely with foil if it browns too quickly.
Rest: Remove from oven and let the pastitsio rest at least 20 minutes before cutting and serving to allow layers to set.
