Brown the ground beef and onion in a large pot over medium-high heat until the beef is no longer pink and the onion is soft. Drain excess fat if desired.
Add the minced garlic and cook for 1 minute.
Stir in the beef broth, diced tomatoes with their juices, tomato paste, potatoes, beef base or Worcestershire sauce, and Italian dressing mix.
Bring the soup to a boil. Reduce the heat, cover, and simmer for 10 minutes.
Stir in the mixed vegetables. Continue simmering for 12–15 minutes, until the potatoes and vegetables are tender.
Taste and adjust with salt, oregano, and black pepper before serving.