For the meat sauce:
Heat the olive oil in a large skillet or pot. Add the ground meat and cook, stirring, until browned. Push the meat to the side and add the onion and garlic. Sauté until translucent, then mix everything together.

Add the tomato sauce, wine (if using), a little sugar (if using fresh tomatoes), cinnamon stick, bay leaf, sweet paprika, nutmeg, salt, and pepper. Stir well and simmer for about 30 minutes, until the sauce thickens.

For the béchamel:
In a saucepan, melt the butter and add the flour, stirring constantly for 1-2 minutes. Gradually add the milk, whisking continuously to prevent lumps. Once the sauce thickens, remove from heat and add the egg, salt, pepper, sweet paprika, nutmeg, and cheese. Mix well. Return to the heat and bring to a gentle boil, stirring.

For the pasta:
In a large pot, bring salted water to a boil. Add the pasta and cook according to package instructions. Drain and set aside.

To assemble the pastitsio: In a baking dish, spread half of the pasta. Sprinkle with some cheese and a little béchamel if desired. Add the remaining pasta, then spread the meat sauce on top. Cover with the béchamel and sprinkle with more cheese if you like.