Begin by heating 1 tablespoon of olive oil in a large, heavy-bottomed pot set over medium-high heat. Add the ground beef and crumble it as it cooks, stirring occasionally, until fully browned. Once cooked through, drain off the excess fat and transfer the beef to a plate. Set aside.
In the same pot, pour in the remaining tablespoon of olive oil. Add the chopped onion, diced carrots, and celery. Sauté the vegetables over medium-high heat for about 6 minutes or until they begin to soften and release their aroma. Stir in the minced garlic and cook for an additional minute, letting the flavors meld.
Return the browned beef to the pot. Add in the tomato sauce, chicken broth, diced tomatoes with their juices, and 1/2 cup of water. Stir in the sugar, basil, oregano, thyme, and marjoram. Season generously with salt and freshly ground black pepper. Bring the mixture to a gentle boil, then reduce the heat to medium-low. Cover with a lid and let the soup simmer for 15 to 20 minutes, stirring occasionally, until the vegetables become tender.
Meanwhile, cook the ditalini pasta separately according to the package instructions. Be sure to cook it to al dente for the best texture, then drain and set aside.
Once the vegetables are soft, stir the cooked pasta into the soup along with the rinsed kidney beans and great northern beans. If the soup appears too thick, add additional broth or water to achieve your desired consistency. Let everything heat through for about 1 more minute.
Finish by stirring in the fresh parsley just before serving. Ladle the soup into bowls and top with a generous sprinkle of finely shredded Romano or Parmesan cheese. Serve warm.