In a cup, combine soy sauce, cornstarch, honey and sherry. Trim and discard any excess fat from steak. Cut the beef lengthwise into 2 strips, then crosswise into 1/2-inch thick slices.
In a wok or 5-quart Dutch oven, heat oil over high heat. Add ginger and stir-fry for 1 minute. Add the beef slices and stir-fry until they are well browned, about 3 minutes. Using a slotted spoon, transfer the beef and ginger to a bowl and set them aside.
Reduce the heat to moderate. Add broccoli and water to the wok. Cover and cook until the broccoli is crisp-tender, about 3 minutes. Add water chestnuts, green onions and the soy-sauce mixture to the broccoli; bring to a boil. Continue cooking, stirring constantly, until the mixture is thickened, about 2 minutes.
Return the beef and any accumulated juices to the broccoli mixture; stir to combine. Season with salt, if desired, and serve immediately.