Cook the pasta in salted water until just almost al dente. Reserve 2 cups of pasta water. Toss the pasta with parmesan, nutmeg, and beaten eggs; set aside.

In a large skillet, sauté diced onion in olive oil until translucent. Add ground beef; cook until no longer pink. Stir in tomato paste, diced tomatoes, cinnamon stick, cloves, allspice, sugar, salt, and pepper. Add reserved pasta water and simmer for 30 minutes.

Prepare béchamel: Melt butter over medium heat. Whisk in flour until combined. Gradually add warm milk, whisking constantly, and season with salt. Bring to a boil, then reduce heat and cook until thickened. Remove from heat, whisk in beaten eggs and parmesan.

Preheat oven to 420°F. Layer half of the pasta in a 9x13-inch baking dish. Spread all meat sauce over pasta. Add remaining pasta on top. Pour béchamel over the assembled dish and sprinkle with grated parmesan.

Bake for 45-50 minutes until golden brown on top. Let cool for 20 minutes before slicing.