Heat a large pot over medium-high heat. Add the ground beef and season with a good pinch of salt and pepper. Cook, breaking apart until the meat is cooked through. Drain off the excess grease if needed. Remove ground beef to a bowl and set aside.
In the same pot, add 2 tbsp of olive oil and heat over medium heat until it shimmers. Add the onion and season with salt and pepper. Sauté onion until it is translucent and soft. Add the garlic and cook for one minute longer. Add the dried spices and cook for one more minute until the spices are fragrant.
Return the ground beef to the pot and add the tomato paste. Cook over low heat, stirring until the tomato paste is incorporated into the ground beef and onion mixture. Add the crushed and diced tomatoes, the chicken broth, bay leaves, and the sugar. Bring the soup to a boil over medium-high heat, then turn down so that it is simmering. Simmer for 15-20 minutes.
In the meantime, add the three cheeses to a small bowl and mix together. Set aside.
Bring a pot of salted water to a boil and cook the pasta according to the directions and drain.
Taste the soup for seasoning and add salt and pepper as needed.
To serve, place noodles in bowls, spoon the soup over the noodles and top with the cheese mixture and fresh basil.