Cook pasta almost al dente in salted boiling water. Reserve 2 cups of pasta water. Toss pasta with Parmesan, nutmeg, and beaten eggs.
In a large skillet, sauté diced onions in olive oil until translucent. Add ground beef and cook until browned. Mix in tomato paste, diced tomatoes, cinnamon, cloves, allspice, sugar, salt, and pepper. Simmer for 30 minutes, adding pasta water if needed.
Make béchamel: Melt butter, whisk in flour, then gradually add warm milk while stirring constantly. Season with salt. Cook until thickened. Add beaten eggs and cook for 2 more minutes.
Preheat oven to 420°F. Layer pasta, meat sauce, and béchamel in a baking dish. Top with grated Parmesan. Bake for 45-50 minutes until golden and bubbling. Cool 20 minutes before serving.
Notes
Enjoy this traditional Greek comfort food with a fresh salad.