Add onion, garlic, carrots, and celery to the pot. Cook until vegetables are softened, about 5 minutes.
Add potatoes, beef broth, diced and crushed tomatoes, Worcestershire, basil, and oregano to the pot. Bring to a boil, then reduce heat and simmer for 20 minutes.
Stir in frozen mixed vegetables and continue to simmer for another 10 minutes or until all vegetables are tender.