In a bowl, combine oyster sauce, sesame oil, sherry, soy sauce, sugar, and cornstarch until sugar and cornstarch are dissolved.
Place steak pieces in a large, shallow bowl. Pour over the oyster sauce mixture and coat steak pieces completely. Refrigerate to marinate for at least 30 minutes.
Add vegetable oil in a large skillet or wok over medium-high heat. Add ginger and garlic and stir. Allow them to sizzle in the hot oil to flavor it, about 1 minute. Remove and discard ginger and garlic.
Add the broccoli and stir until vibrant green and slightly tender, about 5 to 7 minutes. Take the broccoli out and set it aside.
Add more oil into the wok if needed. Add the beef and marinade. Stir until the meat has browned, and the sauce is reduced into a glaze, about 5 minutes.
Add the cooked broccoli. Stir meat and broccoli until heated through, about 3 minutes.