Heat the oil in a large pot over medium-high heat. Add the ground beef and let it brown well before breaking it into smaller pieces. Continue cooking until no longer pink. Drain excess fat if needed.
Add the onion, carrots, and celery. Cook for about 4–5 minutes, stirring occasionally, until the onion begins to soften.
Add the garlic and cook for about 30 seconds. Stir in the tomato paste and cook for another minute, mixing it well with the beef and vegetables.
Pour in the beef broth and add the potatoes. Bring to a gentle boil, then reduce the heat, partially cover the pot, and simmer for 10 minutes, until the potatoes have started to soften.
Stir in the diced tomatoes with their juices, Worcestershire sauce, Italian seasoning, paprika, bay leaf, salt, and black pepper. Return to a gentle simmer, partially cover, and cook for about 15–20 minutes, or until the potatoes are fully tender.
Add the frozen green beans directly to the soup without thawing. Cook for about 5 minutes, just until heated through and tender.
Remove the bay leaf. Taste the broth and adjust the salt and black pepper if needed. Let the soup rest for a few minutes, then ladle into bowls and serve hot.