Whisk oyster sauce, sherry, sesame oil, soy sauce, sugar, and cornstarch together in a bowl; stir until sugar has dissolved.

Place steak in a shallow bowl. Pour oyster sauce mixture over meat and stir to coat; cover and marinate in the refrigerator for at least 30 minutes.

Heat vegetable oil in a wok or large skillet over medium-high heat. Add ginger and garlic; let sizzle for about 1 minute to flavor oil, then remove and discard. Stir in broccoli. Toss and stir until bright green and almost tender, 5 to 7 minutes. Remove broccoli from the wok and set aside.

Add a little more oil to the wok, if needed, then add beef with marinade. Stir and toss until sauce thickens and turns shiny and meat is no longer pink, about 5 minutes. Return broccoli to the wok; stir until heated through, about 3 minutes.