Cut beef steak lengthwise in half, then crosswise into 1/8 to 1/4-inch thick strips. Combine 1/4 cup dressing and beef in medium bowl. Cover and marinate in refrigerator 30 minutes to 2 hours.
Heat 1 tablespoon oil in large nonstick skillet over medium-high heat until hot. Add green beans; stir-fry 5 minutes. Add remaining 1 tablespoon oil and potatoes; continue stir-frying 4 to 6 minutes or until potatoes and green beans are heated through and starting to brown. Remove from skillet; keep warm.
Heat same skillet over medium-high heat until hot. Add 1/2 of beef; stir-fry 1 to 3 minutes or until outside surface of beef is no longer pink. (Do not overcook.) Remove from skillet; add to vegetable mixture. Repeat with remaining beef.
Add remaining 1/4 cup dressing to beef and vegetables; toss to coat thoroughly. Season with salt and pepper, as desired. Serve warm or at room temperature.