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Whisk together the oyster sauce, sesame oil, sherry, soy sauce, sugar, and cornstarch in a bowl, and stir until the sugar has dissolved.
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Place the steak pieces into a shallow bowl, pour the oyster sauce mixture over the meat, stir to coat well, and marinate for at least 30 minutes in refrigerator.
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Heat vegetable oil in a wok or large skillet over medium-high heat, and stir in the ginger and garlic. Let them sizzle in the hot oil for about 1 minute to flavor the oil, then remove and discard.
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Stir in the broccoli, and toss and stir in the hot oil until bright green and almost tender, 5 to 7 minutes. Remove the broccoli from the wok, and set aside.
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Pour a little more oil into the wok, if needed, and stir and toss the beef with the marinade until the sauce forms a glaze on the beef, and the meat is no longer pink, about 5 minutes.
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Return the cooked broccoli to the wok, and stir until the meat and broccoli are heated through, about 3 minutes