In a bowl, toss the sliced steak with 1 tbsp soy sauce and the cornstarch. Let it sit while you prep the veggies and sauce.
In a small bowl, whisk together the remaining soy sauce, oyster sauce, brown sugar, beef broth, and sesame oil. Set aside.
Heat 1 tbsp oil in a large skillet or wok over medium-high heat. Add broccoli florets and stir-fry for 2–3 minutes until bright green and just tender. Remove to a plate.
Add the remaining oil, then the beef in a single layer. Sear for 2 minutes, flip, and cook another 1–2 minutes until just browned.
Toss in garlic and ginger, stir for 30 seconds until fragrant. Return broccoli to the pan, pour in the sauce, and stir everything together. Cook for another 2–3 minutes until the sauce thickens and everything’s coated.
Spoon over hot rice and sprinkle with sliced green onions!