Slice the beef thinly against the grain. Soak it in water for 5 minutes, then squeeze out the excess water to remove myoglobin, which helps reduce any unpleasant or metallic taste.
In a large bowl, add all the marinade ingredients to the beef. Massage well until the liquid is fully absorbed and the beef looks plump and glossy. Add ½ tbsp oil at the end and mix into the beef to lock in the moisture. Let it marinate for 20 minutes.
In a small bowl, mix all the sauce ingredients. Set aside.
Bring a pot of water to a boil. Add a pinch of salt and a splash of oil. Blanch broccoli florets for 30–60 seconds, then drain and set aside.
Heat 2–3 tbsp of oil in a wok or skillet over medium-high heat. Add the beef in a single layer and let it sear for 30–60 seconds without moving. Stir-fry until the beef is mostly cooked, then remove from the pan and drain any excess oil.
In the same pan, add a little more oil if needed. Sauté the ginger and garlic for 30 seconds until fragrant. Add the broccoli and stir-fry for another 30 seconds. Return the beef to the pan, pour in the sauce, and stir-fry everything over high heat until the sauce thickens and coats all the ingredients, about 1 minute.
Drizzle with 1 tsp sesame oil, give it a final toss, and serve immediately over steamed rice.