In a large pan, sauté chopped onions in olive oil until translucent, then add ground beef and brown thoroughly.
Add garlic and tomato paste, stirring for 2 minutes before deglazing the pan with red wine.
Stir in crushed tomatoes, cinnamon stick, cloves, salt, and pepper. Simmer on low heat for 30-40 minutes until the liquid is absorbed.
Boil the pasta in salted water until 2 minutes short of al dente; drain and toss with lightly beaten egg whites and 100g of grated cheese.
For the béchamel, melt butter in a saucepan, whisk in flour for 1 minute, then gradually add milk while whisking constantly until thickened.
Remove béchamel from heat and whisk in egg yolks, nutmeg, and 50g of grated cheese.
Preheat oven to 180°C (350°F).
In a deep 9x13 inch baking dish, layer the pasta, then spread the meat sauce evenly over the top.
Pour the béchamel sauce over the meat layer and sprinkle with the remaining 100g of grated cheese.
Bake for 45-50 minutes until the top is golden brown. Let rest for at least 30 minutes before slicing.