Preheat the oven to 180°C (350°F) and generously grease a 9x13-inch baking dish with Unsalted butter.
Bring a large pot of water to a boil, salt it, and cook the No. 2 macaroni until just al dente (about 1–2 minutes less than package directions). Drain and return to the pot; while hot, toss with the lightly beaten Egg whites, half of the grated Kefalotyri cheese and a pinch of Salt to coat and help the pasta hold together.
Make the meat sauce: heat Olive oil in a large skillet over medium heat, add the chopped Onion and minced Garlic and sauté until softened. Add the Ground beef and cook until nicely browned, breaking it up with a spoon.
Deglaze the pan with Dry red wine, then stir in the Canned crushed tomatoes, Tomato paste, Cinnamon stick, Whole allspice berries, Bay leaves, Dried oregano, a good pinch of Salt, freshly ground Black pepper and a small pinch of Sugar to balance the acidity. Reduce heat and simmer, uncovered, for 25–35 minutes until thick and flavorful; remove and discard the cinnamon, allspice and bay leaves.
Assemble the layers: spread about one-third of the meat sauce on the bottom of the prepared dish, top with the macaroni mixture and press it gently into an even layer, then spoon the remaining meat sauce over the pasta.
Prepare the béchamel: melt 2–3 tablespoons of Unsalted butter in a saucepan over medium heat, whisk in an equal amount of All-purpose flour to form a smooth roux and cook for 1–2 minutes without browning. Gradually whisk in warmed Whole milk and cook, stirring constantly, until the sauce thickens to a creamy pouring consistency.
Remove the béchamel from the heat and temper in the beaten Eggs a little at a time, then stir in the remaining grated Kefalotyri cheese, a generous pinch of Ground nutmeg, Salt and a little White pepper. Pour the béchamel over the assembled pasta and meat so it covers evenly.
Sprinkle the top with Breadcrumbs and an extra scattering of grated kefalotyri if desired. Bake at 180°C (350°F) for 40–50 minutes, until the top is puffed and golden-brown. Let the pastitsio rest for 15–20 minutes before slicing so the layers set for clean serving.
