Prepare the steak- Slice the steak into thin strips and season with salt and pepper. Mix 2 tablespoons of cornstarch with a few tablespoons of water until dissolved and coat the steak in the mixture. Heat a large skillet over medium-high heat, add oil, and let it get hot before adding the steak strips. Fry the steak strips for a few minutes, stirring occasionally.
Prepare the sauce- In a bowl, mix together the shoyu, brown sugar, oyster sauce, garlic, ginger and remaining cornstarch until combined. Heat a small pan over medium heat and add the sauce mixture. Stir constantly until it starts to thicken and remove from heat.
Make the dish- Add the broccoli and onion to the skillet with the steak strips and cook until the vegetables are tender about 5 minutes. Pour in the sauce over everything and stir until combined. Cook for a few more minutes so that everything is warmed through.
Serve- Serve the Hawaii Beef Broccoli with freshly cooked rice.