Heat oil in a 4 or 5-qt. saucepan or Dutch oven over high heat. Add steak; season with salt and pepper, and cook about 8 minutes or until very well browned all over.
Add onion and cook over medium-high heat, stirring occasionally, about 4 minutes or until soft. Add mushrooms, garlic and thyme; cook about 5 minutes, stirring occasionally, or until soft.
Stir in broth, tomatoes, potatoes and green beans. Cover and bring to a boil over high heat. Uncover; reduce heat to medium-low, and simmer 10 to 15 minutes until vegetables are tender. Season to taste with salt and pepper. Garnish with parsley, if desired.