Whisk sherry, oyster sauce, sesame oil, soy sauce, sugar, and cornstarch together in a bowl until sugar dissolves.
Arrange steak slices in a shallow bowl, pour the oyster sauce mixture over the meat, stir to coat, and refrigerate at least 30 minutes.
Heat vegetable oil in a wok or large skillet over medium-high heat. Cook and stir ginger and garlic in hot oil until fragrant about 1 minute. Remove and discard the ginger and garlic. Stir broccoli, mushrooms, and snow peas together in the skillet; cook and stir in the hot oil until the broccoli is bright green and almost tender, 5 to 7 minutes. Remove the vegetable mixture to a bowl.
Pour beef slices with the marinade into the skillet; cook and stir until the sauce forms a glaze on the beef and the meat is no longer pink, about 5 minutes. Return the cooked vegetables to the wok; cook and stir until the broccoli is heated through, about 3 minutes.