Heat olive oil in a large soup pot over medium-high heat. Add ground beef and cook until browned, breaking it up as it cooks. Drain excess grease if needed.
Add onion, carrots, and celery. Cook 5 to 6 minutes, until onion is soft. Add garlic and cook 30 seconds.
Stir in Italian seasoning, paprika, thyme, salt, and pepper. Add tomato paste and cook 1 minute, stirring constantly.
Add diced tomatoes, tomato sauce, beef broth, Worcestershire sauce, and bay leaf. Stir and scrape any browned bits from the bottom of the pot.
Add diced potatoes. Bring to a gentle boil, then reduce heat to simmer. Cover and cook 15 minutes.
Add green beans, corn, and peas. Cover and simmer 10 to 12 minutes, until potatoes are fork-tender.
Remove bay leaf. Taste and adjust seasoning. Serve hot with parsley and toppings if desired.