Slice steak with the grain into 2-inch wide strips. Then slice the strips across the grain into ¼ inch thick slices.
Whisk together soy sauce, cornstarch, wine/vinegar, sugar and black pepper in a medium bowl. Add steak strips and mix well. Let sit for 10 minutes.
Heat 2 tbsp of oil in pan over high heat until oil is hot but not smoking. Add green beans and stir for 1 minute. Add water and reduce heat to medium. Cover and cook until tender-crisp, 6–9 minutes. Transfer beans to a medium bowl.
Add ¼ cup of oil to pan over high heat. Add onion and ginger, and stir constantly for 1 minute. Add all of the beef mixture to the pan. Cook, stirring, until steak is no longer pink, about 2 minutes.
Return green beans to pan, stir until all is mixed well together.