In a large pot or Dutch oven, brown the ground beef over medium heat until fully cooked. Drain any excess fat.
Add the diced onion, carrots, celery, and minced garlic to the pot with the ground beef. Cook until the vegetables are tender, about 5-7 minutes.
Stir in the diced tomatoes (with liquid), tomato sauce, kidney beans (with liquid), and cannellini beans (with liquid).
Pour in the V8 juice, then add the white vinegar, salt, oregano, basil, thyme, black pepper, and red pepper flakes (if using). Stir well to combine all ingredients.
Bring the soup to a boil, then reduce the heat to low. Cover the pot and let it simmer for 30 minutes, stirring occasionally.
While the soup simmers, cook the ditalini pasta according to package instructions until al dente. Drain and set aside.
Once the soup has simmered, stir in the cooked pasta. Let the soup simmer for an additional 5 minutes to allow the flavors to meld. Taste and adjust seasoning if necessary.
Ladle the soup into bowls and serve hot. Optionally, top with grated Parmesan cheese and fresh herbs.