Heat the oven to 375°F. Grease an 8×8-inch glass or ceramic baking dish with butter or cooking spray.
Boil the pasta in a large pot of salted water according to the package directions. Drain in a colander.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the ground beef, onion, garlic, ½ teaspoon salt, and pepper and cook, stirring occasionally, until the meat is browned. Add in the wine (and perhaps pour a glass for the cook!) and scrape up any of the bits stuck to the pan with your spoon. Stir in the tomatoes, parsley and another ¼ teaspoon salt, and let the mixture simmer until most of the liquid has evaporated. Remove from the heat and set aside.
Transfer half of the pasta to the prepared baking dish, spreading it in an even layer all over the bottom of the dish. Next, spread the meat mixture in an even layer on top of the pasta. Finally, top the meat with an even layer of the remaining pasta.
To make the béchamel, melt the butter in a medium saucepan over medium heat. Whisk in the flour to form a thick paste and cook, whisking occasionally, until the aroma of the mixture is more nutty than floury, 1 to 2 minutes. Reduce the heat to medium-low and whisk in the milk, then the beaten egg. Mix in half of the Parmesan, and the salt and pepper. Taste the sauce and adjust the seasoning if needed. The sauce should be somewhat thick, like a light custard.
Sprinkle the remaining Parmesan over the pasta in the baking dish. Top the Parmesan with the béchamel, spreading the sauce to the edges. The béchamel should form its own layer on top of the casserole.
Bake until the béchamel is set and browned on top, 45 to 50 minutes. The casserole will be easier to cut—and see those lovely layers—if you wait for it to cool a bit.
Notes
Find pastitsio (aka pastichio) pasta, which is long and tubular, in international and specialty food stores or online, such as on Amazon.com. Bucatini or penne are suitable substitutes.
This recipe can easily be doubled. Use a 9x13 inch pan.