Slice the flank steak thinly against the grain. In a bowl, toss the steak with baking soda and water. Let marinate for 15 minutes to velvet and tenderize the meat, then rinse quickly and pat dry.
In a small bowl, whisk together the soy sauce, oyster sauce, brown sugar, sesame oil, garlic, ginger, cornstarch, and beef broth to create the stir-fry sauce.
Bring a pot of water to a boil and blanch the broccoli florets for 1 to 2 minutes until bright green. Drain well and set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over high heat. Add the sliced beef in a single layer, cooking for 2 to 3 minutes until browned on both sides. Remove beef from the pan and set aside.
Add the remaining 1 tablespoon of oil to the pan, then add the blanched broccoli. Stir-fry for 1 minute to blister slightly.
Pour the prepared sauce into the pan with the broccoli, stirring continuously until it begins to thicken and bubble.
Return the cooked beef to the skillet. Toss everything together for 1 to 2 minutes until the beef and broccoli are evenly coated in the glossy sauce. Serve immediately over warm rice.