In a mixing bowl, combine the sliced flank steak with 2 tablespoons of soy sauce and 1 tablespoon of cornstarch. Mix well and let it marinate for 10 minutes.
While the beef is marinating, prepare the broccoli by blanching it in boiling water for 2 minutes, then immediately transferring it to cold water to retain the color and crunch. Drain and set aside.
Heat 1 tablespoon of vegetable oil in a wok or large skillet over medium-high heat. Add the marinated beef and stir-fry for about 3-4 minutes until browned and cooked through. Remove the beef from the wok and set it aside.
In the same wok, add the remaining tablespoon of oil. Stir in the minced garlic and ginger, cooking for about 30 seconds until fragrant.
Add the blanched broccoli and stir-fry for another 2 minutes.
Return the beef to the wok, and add the beef broth, oyster sauce, the remaining soy sauce, sesame oil, and salt and pepper. Stir everything together, cooking for an additional 2-3 minutes until heated through, and the sauce has thickened slightly.
Serve hot over cooked rice.