Pour soy sauce, cornstarch, rice vinegar, sugar, and black pepper into a bowl. Mix well.
Slice steak with the grain into 2-inch-wide strips. Then slice the strips across the grain into thin slices. Place in bowl. Using your hands, toss the meat and seasonings together to mix well.
Heat 1 Tbsp oil in a wok or stir fry pan over high heat until hot but not smoking. Add green beans and stir for about 1 minute. Add water and reduce heat to medium. Cover and cook until crisp-tender or about 6-9 minutes.
Add remaining oil to pan and increase heat to high. Add ginger, onion, and peppers to pan and stir constantly for 2-3 minutes. Add beef mixture and cook until meat is no longer pink, about 2 minutes.
Return beans to pan and mix well until heated thoroughly, about 1 minute.