For the Beef and Marinade: Using your hands, in a medium sized bowl, combine the steak with marinade ingredients. Massage the marinade into the meat for at least 30 seconds. Cover steak and let marinate for at least 30 minutes to one hour, or refrigerate up to overnight.
For the Sauce: Using a small bowl, mix together both soy sauces, oyster sauce and the sugar. In a small separate dish, mix together the cornstarch and water making the cornstarch slurry. Add in the cornstarch slurry into the sauce and mix until everything is combined. Set aside.
For the Broccoli: Heat a cup of water in a wok over high heat until boiling. Add the broccoli and cover with lid. Let cook until tender-crisp, for about 1 to 2 minutes only. Drain and transfer to a plate.
For the Stir-Fry: Wipe out your wok if you need to. Heat your wok over high heat until lightly smoking. Add the vegetable oil and swirl to coat. Add your marinated beef, spread into a single layer and let it cook until lightly seared, for about 30 seconds to 1 minute. Continue to stir-fry and toss in the wok until the beef is mostly cooked through. Immediately add the garlic and ginger and stir-fry until fragrant, about 30 to 45 seconds longer.
Add 1 tablespoon Shaoxing wine by pouring it around the side of the wok. Pour in the sauce mixture and and toss to combine. Add in the broccoli and toss to combine again, coating the broccoli in the sauce, for about 1 minute or so. If the sauce seems thin, turn up the heat and reduce it further, or add a bit more cornstarch slurry. If the sauce is too thick, add a splash of water. Transfer to a serving platter and enjoy immediately with steamed white rice.