Heat the olive oil in a stock pot over medium-high heat; cook the beef in the hot oil until completely browned, 7 to 10 minutes. Add the onion and bay leaves, reduce heat to medium, cook until the onion is softened, 5 to 7 minutes. Use a wooden spoon to scrape any bits stuck to the bottom of the pot. Stir the carrots, potatoes, and beef stock into the mixture; bring to a simmer and cook until the vegetables are just barely tender, about 5 minutes.
Stir the green beans, corn, peas, zucchini, cabbage, tomatoes, Italian seasoning blend, garlic powder, salt, and pepper into the beef mixture. Cover the stock pot, reduce heat to medium-low, and simmer the soup until the beef is cooked through and the vegetables are tender, 45 to 50 minutes.
Stir the orzo pasta into the soup; replace the cover to the stock pot and continue cooking until the pasta is tender, about 5 minutes more.