Heat olive oil in a large pot over medium-high heat. Add ground beef and cook until browned, breaking it apart as it cooks, about 6-8 minutes. Drain excess fat if needed.
Add onion, carrots, and celery to the pot. Cook until vegetables are softened, about 6-7 minutes. Add garlic and cook for 1 minute until fragrant.
Pour in beef broth, chicken broth, tomato sauce, and diced tomatoes. Add both types of beans, oregano, basil, thyme, and parmesan rind if using. Bring to a boil, then reduce heat and simmer for 15 minutes.
Add ditalini pasta directly to the soup and cook according to package directions, usually 8-10 minutes, stirring occasionally to prevent sticking.
Remove parmesan rind if used. Season soup with salt and black pepper to taste. Serve hot with freshly grated parmesan cheese and a drizzle of olive oil.