Preheat the oven to 350°F (175°C) and spray a deep 9x13-inch casserole dish with nonstick spray.
Make the béchamel: melt 6 tablespoons butter in a medium saucepan over medium heat. Whisk in 3/4 cup flour and cook briefly, then gradually whisk in the hot milk until smooth and thickened.
Remove the béchamel from heat, stir in 1 1/2 teaspoons salt, and let it cool until lukewarm. Whisk in 3 whole eggs until combined and set aside.
Prepare the meat sauce: melt 4 tablespoons butter in a large skillet over medium heat. Add the chopped onions and sauté until softened and golden.
Add the ground beef to the skillet and cook, breaking up lumps, until browned. Stir in 1/8 teaspoon ground cinnamon and salt and pepper to taste.
Stir in 1/2 cup water and 2 tablespoons tomato paste, simmer for about 5 minutes to meld flavors, then remove from heat and set aside.
Cook the ziti according to package directions until al dente. Drain, rinse with cool water, and when cooled stir in the 3 beaten eggs and 1 1/2 teaspoons salt.
Assemble the pastitsio: place half of the egged pasta in the bottom of the prepared dish. Sprinkle generously with about one-third of the grated cheese.
Spoon the meat sauce in an even layer over the pasta, then sprinkle another portion of cheese over the meat.
Add the remaining pasta on top of the meat layer and sprinkle with more cheese. Pour the béchamel sauce evenly over the top and finish by sprinkling with the remaining cheese.
Bake for 45 minutes, or until the top is bubbly and golden. Let the pastitsio rest at room temperature for at least 20 minutes before slicing to help the layers set.