In a bowl, toss sliced beef with cornstarch and 1 tablespoon of soy sauce. Set aside to marinate for 10 minutes.
In a separate bowl, whisk together oyster sauce, hoisin sauce, remaining soy sauce, brown sugar, sesame oil, garlic, and ginger.
Heat 1 tablespoon of olive oil in a skillet or wok over medium-high heat. Sauté beef until browned, about 2–3 minutes. Remove and set aside.
Add the remaining olive oil and broccoli to the pan. Stir-fry for 2 minutes, then add water and cover for 2–3 minutes to steam until tender-crisp.
Return the beef to the pan, pour in the sauce, and stir everything together. Cook for another 2 minutes until well coated and heated through.
Serve hot over rice.