Slice steak into very thin strips about 3 inches long. Toss with marinade mixture in a large zip top bag until evenly coated, and allow to marinade overnight if possible.
Stir fry the beef quickly in small batches until browned. Remove from the pan.
Stir fry the broccoli and onions until the broccoli is bright green and slightly softened.
While it cooks, mix the sauce in a large liquid measuring cup, whisking to combine.
Add the cooked beef back to the pan, and pour the sauce over everything.
Bring the sauce to a boil to thicken and toss to coat evenly.
Serve over cooked white rice.