In a bowl, combine soy sauce, cornstarch, sesame oil, and black pepper. Add the thinly sliced beef, mix well, and let it marinate for at least 10 minutes.
Bring a pot of water to a boil. Blanch the broccoli for 2 minutes, then drain and rinse under cold water to keep it crisp.
Heat vegetable oil in a large pan or wok over medium-high heat. Add the marinated beef and cook for 2-3 minutes until browned. Remove from the pan and set aside.
In the same pan, sauté garlic and ginger for 30 seconds. Add beef broth, oyster sauce, soy sauce, and brown sugar. Stir in the cornstarch slurry to thicken. Return the beef and broccoli to the pan, tossing everything in the sauce until well-coated.