Cook pasta just almost al dente in salted water. Reserve 2 cups pasta water. Toss pasta with parmesan, nutmeg, and eggs; set aside.
In a large pot, heat olive oil. Add onion and sauté until translucent, about 3 minutes. Add ground beef; cook until no longer pink. Mix in tomato paste, diced tomatoes, spices, sugar, and salt and pepper. Add 2 cups of pasta water; simmer for 30 minutes, stirring occasionally.
In a medium pot, melt butter over medium-high heat. Whisk in flour. Gradually add warm milk, whisking constantly. Season with salt. Bring to a boil, cook 2 minutes until thickened. Whisk in beaten eggs, cook 2 more minutes.
Preheat oven to 420°F. Transfer half of pasta to a 9x13 baking dish. Spread meat sauce evenly on top, then remaining pasta. Pour béchamel over pasta, spread evenly. Sprinkle with grated parmesan cheese.
Bake for 45-50 minutes until golden. Cool for 20 minutes before slicing.
Notes
Serve hot with a side of Greek salad for a complete meal.