Here the broiler does all the work, as opposed to the more traditional, hands-on method of stir-frying in a wok or skillet.
Preheat broiler with rack 4 inches from heating element. Stir together oyster sauce, soy sauce, sesame oil, garlic, ginger, cornstarch, and 1 tablespoon water in a large bowl. Season with salt and pepper. Stir in beef and broccoli to evenly coat. Spread mixture in a single layer on a rimmed baking sheet.
Broil, rotating sheet halfway through, until beef is sizzling and browned in places and broccoli is charred and crisp-tender, 8 to 10 minutes. Stir in water chestnuts. Serve over rice, drizzled with pan juices and sprinkled with sesame seeds.