In a saucepan over medium-high heat, brown half of the ground beef at a time in half of the olive oil, breaking it apart with a wooden spoon. Return the meat to the saucepan. Add onion and garlic. Cook for 5 minutes. Season with salt and pepper. Add tomato paste and spices. Cook for 1 minute while stirring. Deglaze with red wine. Add tomatoes and broth. Simmer until the sauce is nearly dry, about 10 minutes. Adjust seasoning. Keep warm.

Place the rack in the center of the oven. Preheat oven to 180°C (350°F). Lightly grease a 13 x 9 inch baking dish.

In a second saucepan over medium heat, melt butter. Add flour and cook for 1 minute, whisking. Gradually add milk while whisking. Add nutmeg. Bring to a boil while stirring constantly. Reduce to a simmer for 1 minute or until mixture thickens. Remove from heat. Stir in cheese and egg yolks. Adjust seasoning. Keep warm.

Meanwhile, in a third pot of boiling salted water, cook the pasta al dente. Drain. Return pasta to the pot. Add 250 ml (1 cup) of béchamel, egg whites, and cheese. Mix well. Spread the pasta in the baking dish, pressing down firmly to minimize empty spaces.

Pour the meat sauce over the pasta and evenly spread with a spatula. Pour the remaining béchamel over the meat sauce. Bake for 1 hour or until the béchamel is golden brown. Let rest for 15 minutes before serving.