Brown the beef: In a large pot over medium heat, cook ground beef until browned and fully cooked. If using stew beef, sear on all sides until browned. Remove and set aside.
Sauté aromatics: In the same pot, add olive oil if needed and cook onion, garlic, carrots, and celery for 5–7 minutes until slightly softened.
Add potatoes and tomatoes: Stir in cubed potatoes and diced tomatoes. Let everything cook together for a couple of minutes to blend flavors.
Pour in broth and seasonings: Add beef broth, salt, pepper, Italian seasoning, bay leaf, and return beef to the pot. Stir to combine.
Simmer: Bring to a boil, then reduce heat and simmer for 30–40 minutes, or until the vegetables are tender and the flavors have developed.
Add peas and green beans: Stir in frozen peas and green beans (or corn) and simmer for 5–10 more minutes until everything is hot and just tender.
Taste and finish: Remove the bay leaf. Taste the soup and adjust seasoning if needed. Garnish with chopped parsley before serving.