Coat beef with flour, shaking off excess. In a large nonstick stock pot, heat oil over medium-high heat; add beef and saute until brown, approximately 5 minutes. Remove beef from stock pot and set aside.
Add onions and mushrooms to stock pot and cook gently for 5 minutes. Add garlic and cook for 1 minute, continually stirring.
Return cooked beef to pot; stir in tomato puree and stock. Add enough water to just cover ingredients and bring to the boil. Reduce heat to low and simmer until beef is tender, about 1 hour and 15 minutes.
Skim off any foam that has accumulated on the surface of stew; add carrots, potatoes and green beans. Cover partially and simmer for 15 minutes.
In a small mixing bowl, mix cornflour and cold water. Stir mixture into stew. Increase heat and boil uncovered for 1 minute. Sprinkle with parsley and serve.