Preheat your oven to 180°C (350°F). To start the meat sauce, heat olive oil in a skillet over medium heat. Add the chopped onion and garlic, sautéing until soft and fragrant, about 3-4 minutes.

Add the ground meat to the skillet, breaking it up with a spoon. Cook until browned, about 5-7 minutes. Stir in the crushed tomatoes, tomato paste, red wine (if using), cinnamon, and oregano. Season with salt and pepper. Simmer the sauce for 15-20 minutes until thickened, then set aside.

For the pasta, cook according to package instructions in salted water, draining when al dente. Transfer the cooked pasta to a large bowl, add butter, and mix well. Let cool slightly before adding the beaten egg and cheese, stirring to coat evenly.

To prepare the béchamel sauce, melt butter in a saucepan over medium heat. Add flour, whisking continuously for 2-3 minutes until lightly golden, which removes the raw flour taste.

Gradually whisk in the warmed milk, continuing to stir until the sauce thickens, about 5-7 minutes. Stir in the cheese, nutmeg, salt, and pepper. Remove from heat and allow to cool slightly before mixing in the beaten egg, ensuring a creamy and smooth béchamel.

Assemble the Pastitsio in a lightly greased baking dish. Spread half of the pasta mixture evenly at the bottom of the dish. Spoon the meat sauce over the pasta layer, spreading it to cover evenly. Layer the remaining pasta on top.

Pour the béchamel sauce over the top pasta layer, spreading it with a spatula. The béchamel should cover the entire surface, creating a creamy top layer that will bake to a golden crust.

Bake the Pastitsio in the preheated oven for 45-50 minutes, or until the top is golden and bubbling. Let rest for 10 minutes before slicing. Serve warm, garnished with extra grated cheese or fresh parsley if desired. This comforting, aromatic dish pairs wonderfully with a crisp green salad or roasted vegetables.