Marinate the beef: In a bowl, combine sliced beef with soy sauce, cornstarch, and sesame oil. Toss to coat and let marinate for 10–15 minutes while preparing other ingredients.
Prepare the sauce: In a small bowl, whisk together soy sauce, oyster sauce, brown sugar, garlic, ginger, and broth. Set aside.
Cook the broccoli: Heat 1 tbsp vegetable oil in a large skillet or wok over medium-high heat. Add broccoli (and carrot slices if using) and stir-fry for 2–3 minutes until bright green and crisp-tender. Remove vegetables from the pan and set aside.
Cook the beef: Add remaining 1 tbsp oil to the pan. Add marinated beef in a single layer. Stir-fry for 2–3 minutes until browned but not overcooked.
Combine and add sauce: Return the vegetables to the pan. Pour in the prepared sauce and bring to a simmer. Stir in cornstarch slurry and cook 1–2 minutes until sauce thickens and coats beef and broccoli evenly.
Serve: Serve immediately over steamed rice. Garnish with sesame seeds and sliced green onions, if desired.