Marinate the Beef:
In a medium bowl, combine beef slices with soy sauce, cornstarch, and sesame oil. Toss well and set aside for at least 15 minutes while you prepare other ingredients.
Prepare the Sauce:
In a small bowl, whisk together beef broth, soy sauce, oyster sauce, cornstarch, brown sugar, garlic, ginger, and sesame oil until smooth. Set aside.
Blanch the Broccoli:
Bring a pot of water to boil. Add broccoli florets and cook for 1–2 minutes until bright green and slightly tender. Drain immediately and rinse with cold water to stop cooking.
Cook the Beef:
Heat 1 tbsp vegetable oil in a large skillet or wok over medium-high heat. Add beef in a single layer (work in batches if needed) and sear for 1–2 minutes per side until browned but not fully cooked through. Remove beef and set aside.
Combine and Cook:
Add remaining 1 tbsp oil to the skillet. Stir in the blanched broccoli, then return beef to the pan. Pour sauce over and stir-fry for 2–3 minutes until sauce thickens and beef is fully cooked.
Serve:
Garnish with green onions and sesame seeds if desired. Serve hot over steamed rice or noodles.