Start by patting the beef chunks dry with paper towels. Season the beef generously with salt and pepper.
Heat the olive oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the beef in a single layer and let it brown deeply on all sides, about six to eight minutes total. Transfer the beef to a plate and set it aside.
Reduce the heat to medium and add the diced onion to the pot, stirring to scrape up any browned bits. Cook the onion until it has softened and become translucent, about five to six minutes. Add the minced garlic and cook for another minute until fragrant.
Return the browned beef to the pot, along with any accumulated juices. Pour in the beef broth, water, and crushed tomatoes, stirring to combine. Add the bay leaves, dried thyme, dried oregano, and Worcestershire sauce. Bring to a gentle boil, then reduce the heat to low, cover, and let it simmer for one and a half to two hours.
After the beef has become tender, add the carrots, celery, and potatoes. Continue simmering for another twenty to twenty-five minutes, until the vegetables are fork-tender.
Stir in the green beans and corn, and let them cook for about ten minutes more. Add the peas during the last five minutes of cooking.
Remove the bay leaves and discard them. Taste the soup and adjust the seasoning with additional salt and pepper as needed. Let the soup rest for a few minutes off the heat before serving.
Ladle the soup into deep bowls and garnish with fresh parsley. Serve with crusty bread, buttermilk biscuits, or oyster crackers.