In a small bowl, whisk together soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and brown sugar. Set aside.
Heat vegetable oil in a large skillet or wok over medium-high heat.
Add sliced beef and cook until browned, about 3-4 minutes. Remove beef and set aside.
In the same skillet, add garlic and broccoli. Stir-fry for 4-5 minutes until broccoli is tender-crisp.
Return beef to the skillet and pour in the sauce mixture.
Cook, stirring constantly, until sauce thickens and coats beef and broccoli, about 2-3 minutes.
Season with salt and pepper to taste. Serve hot over rice or noodles.