In a bowl, mix soy sauce, brown sugar, cornstarch, garlic, and ginger. Add sliced beef and marinate for 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add marinated beef and cook until browned. Remove from skillet and set aside.
Add remaining vegetable oil and sauté broccoli until bright green and slightly tender.
Return beef to skillet and add beef broth, oyster sauce, sesame oil, and black pepper.
Stir well and cook for another 2-3 minutes until sauce thickens.
Serve hot over white rice.