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 until combined and bubbly.
Gradually whisk in the hot warmed milk and cook, whisking constantly, until the sauce is smooth and thickened.
Stir in 1½ teaspoons salt, remove the pan from heat and let the sauce cool until lukewarm. Whisk in 3 large eggs and set aside.
Make 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, breaking it up, and cook until browned. Stir in 1/8 teaspoon ground cinnamon, salt and pepper to taste, 1/2 cup water, and 2 tablespoons tomato paste. Simmer about 5 minutes, then remove from heat.
Cook the ziti according to package directions until just al dente. Drain, rinse with cool water, and let cool slightly.
When the pasta is cool, stir in the 3 beaten eggs and 1½ teaspoons salt until evenly coated.
Assemble: place half of the pasta in the prepared dish and sprinkle generously with about one-third of the grated cheese.
Spoon the meat mixture in an even layer over the pasta, then sprinkle another portion of the cheese over the meat.
Add the remaining pasta on top of the meat layer and sprinkle with more cheese. Pour the béchamel sauce over everything and finish by sprinkling with the remaining cheese.
Bake for 45 minutes, or until the top is bubbly and golden. Let rest at room temperature at least 20 minutes before slicing to help the layers set.
