In a large Dutch oven, heat 2 tablespoons of olive oil over medium-high heat. Add the stew meat. Season the beef with salt and pepper and brown the beef in batches to avoid overcrowding. Once browned, transfer the beef to a plate and set aside.
In the same pot, add another tablespoon of olive oil. Add the onions, carrots, and celery. Sauté for about 4-5 minutes or until the onions become translucent. Add the minced garlic and sauté for an additional minute.
Pour the beef broth and diced tomatoes (with their juice) into the pot. Return the browned beef to the pot. Add the Italian seasoning, bay leaves, and season with salt and pepper. Bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and let it simmer for about 25 minutes.
Incorporate the diced potatoes into the pot. Let it simmer, covered, for an additional 15 minutes.
Add the green beans to the pot and let it simmer for another 10 minutes or until the green beans are tender but still vibrant in color. Stir in the corn and let it cook for 5 more minutes or until heated through.
Turn off the heat. Stir in the freshly chopped parsley. Taste and adjust the seasoning if necessary.
Ladle the soup into bowls and serve warm with crusty bread or a side salad if desired.