Whisk soy sauce, oyster sauce, brown sugar, cornstarch slurry, and water.
Heat 1 tablespoon oil over high heat. Brown half the steak for about 2 minutes per side, transfer it, and repeat with the remaining steak.
Add remaining oil, broccoli, and 2 tablespoons water. Cover and steam 3 to 4 minutes until crisp-tender.
Uncover, add garlic and ginger, and stir 30 seconds.
Return beef, add sauce, and toss about 2 minutes until bubbling, thickened, and glossy.
Serve over cooked white rice.