Prepare Beef: Season the beef chuck roast pieces with salt and pepper thoroughly.
Brown Beef: Heat olive oil in a large soup pot over medium-high heat. Cook the beef in small batches to ensure thorough browning, about 2 minutes on each side, then set aside.
Cook Onion and Garlic: Lower heat to medium. Add chopped onion and minced garlic to the pot, cooking until onion is soft and garlic is aromatic, about 2 minutes.
Add Liquids and Beef: Return the beef to the pot. Pour in beef broth and add diced tomatoes with juices, along with Italian seasoning. Stir well, loosening any bits stuck to the bottom. Once boiling, reduce to a simmer, cover, and cook until beef is tender, between 45-65 minutes.
Vegetable Time: Incorporate potatoes, carrots, and celery into the pot. Continue simmering for another 15 minutes.
Final Vegetables: Add green beans and corn to the soup, cooking for an additional 10 minutes. For softer beans, add them with the other vegetables earlier.
Adjust and Serve: Taste and adjust seasoning with additional salt and pepper as desired. Garnish with fresh parsley before serving warm.