Warm 1 Tbsp olive oil in a large pot over medium-high heat, then add the ground beef and break it into small pieces as it cooks. Continue until the beef is fully cooked and browned in spots, with no pink meat remaining.
Spoon off and drain the rendered fat, then move the beef to a plate and pour the remaining 1 Tbsp olive oil into the pot. The pot should have a light coating of oil but no heavy layer of grease.
Add the onion, carrots, and celery and cook over medium-high heat for about 6 minutes, then stir in the garlic for 1 minute. The vegetables should look softened and glossy, and the garlic should smell fragrant without browning.
Return the beef to the pot and add the chicken broth, tomato sauce, water, diced tomatoes, sugar, basil, oregano, thyme, marjoram, salt, and pepper. Stir until the tomato sauce loosens into an even, herb-speckled broth.
Bring the soup to a boil, lower the heat to medium-low, cover, and simmer for about 15 to 20 minutes, stirring occasionally. Keep the broth at a gentle bubble until the carrots and celery are fully tender.
While the soup simmers, cook the ditalini according to the package directions and drain it when al dente. Taste a piece shortly before it is done so the center is tender with a slight bite.
Stir the drained pasta, kidney beans, and Great Northern beans into the soup, adding more broth or water if you prefer a looser consistency. The beans should heat through while still holding their shape and the pasta should remain distinct in the broth.
Cook for 1 more minute, then stir in the parsley and serve with Romano or Parmesan cheese. The parsley should stay bright green, and the cheese should melt lightly over the hot soup.