1. Bring a large pot of water to a boil for the noodles. Preheat the oven to 350°.

2. In a large pot, cook the beef and onions over medium-high heat, stirring occasionally and breaking up the meat with a spoon, until the beef is browned and the onions are tender, 7 to 8 minutes. Using a slotted spoon, transfer to a bowl. Drain the fat from the pot.

3. In the same pot, cook the sausage and garlic over medium-high heat, stirring occasionally and breaking up the meat with a spoon, until the sausage is browned, 3 to 5 minutes. Add the tomatoes, tomato puree, and tomato paste. Stir in the basil and cinnamon. Add the beef and onions. Season with salt and pepper. Simmer, stirring often, until the sauce thickens and the flavors meld, about 20 minutes.

4. Salt the boiling water and add the noodles. Cook just to al dente. Drain the noodles.

5. In a large bowl, whisk the eggs. Stir in 4 cups ricotta.

6. To build the lasagna, start by spreading a thin layer of sauce in the bottom of a 10-by-15-inch lasagna pan. Top with a quarter of the noodles in an even layer. Top with a third of the ricotta mixture, a quarter of the Pecorino, and a quarter of the sauce. Repeat the layering 2 more times with the noodles, ricotta mixture, Pecorino, and sauce. Top with the remaining noodles. Cover with the remaining sauce. Top with dollops of the remaining 1 cup ricotta. Sprinkle with the remaining Pecorino. Bake until bubbly, about 45 minutes. Let rest for 10 minutes before serving.