In a medium bowl, combine the sliced beef, soy sauce, oyster sauce, and cornstarch. Mix well and let it marinate for about 10 minutes.
While the beef is marinating, prepare the broccoli by steaming it until it is bright green and slightly tender, about 3-4 minutes. Set aside.
Heat 2 tablespoons of vegetable oil in a wok or large skillet over medium-high heat.
Add the marinated beef to the hot oil in a single layer, cooking for about 2-3 minutes until browned. Stir frequently.
Add the minced garlic and ginger, cooking for an additional minute until fragrant.
Pour in the beef broth, allowing it to simmer for about 1-2 minutes until the sauce thickens slightly.
Add the steamed broccoli to the pan, tossing to combine everything evenly. Cook for another 2 minutes.
Season with salt and pepper to taste.
Serve the beef and broccoli hot over cooked rice.