Begin by marinating the sliced beef. In a bowl, combine the soy sauce, oyster sauce, cornstarch, and sesame oil. Add the sliced beef and toss to coat. Let it marinate for at least 10 minutes while you prepare the broccoli.
If you prefer steamed broccoli, bring water to a boil in a separate pot and steam the broccoli florets for about 3-4 minutes until bright green and tender-crisp. Alternatively, you can stir-fry the broccoli along with the beef.
Heat the vegetable oil in a wok or large skillet over medium-high heat. Add the minced garlic and ginger, and stir-fry for about 30 seconds until fragrant.
Increase the heat to high and add the marinated beef to the wok. Stir-fry for about 3-5 minutes, or until the beef is browned and cooked through.
If using stir-fried broccoli, add it to the wok with the beef now. If you steamed broccoli, remove the beef from the wok and keep it warm while you add the broccoli. Stir everything together.
Pour in the beef broth (or water) and toss to combine. Allow the mixture to simmer for another 1-2 minutes until the sauce thickens slightly.
Serve the beef and broccoli hot over cooked rice.