In a large heavy-bottomed pot or Dutch oven, heat the oil over medium-high heat. Add the ground beef, onion, and celery. Cook, stirring occasionally and breaking the beef into crumbles, until the beef is browned and the vegetables start to soften, about 5 to 7 minutes. Add the minced garlic and cook for an additional 2 minutes.

Stir in the tomato paste, ensuring it evenly coats the beef and vegetables. Cook for about 1 minute. Then, add the diced tomatoes along with their juice, beef broth, Italian seasoning, salt, and pepper. Stir well, scraping the bottom of the pot to lift any browned bits.

Add the cubed potatoes to the pot and bring the mixture to a boil. Once boiling, reduce the heat to medium and let it simmer, uncovered, for about 10 minutes. Stir in the chopped mixed vegetables, making sure everything is submerged. Partially cover the pot and let it simmer until the potatoes and vegetables are tender, about 7 to 10 minutes.

Taste the soup and adjust the seasoning with Worcestershire sauce, additional salt, and pepper as desired. Serve the soup in bowls, garnished with chopped parsley if using.