In a bowl, combine the soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and sugar. Stir until well mixed and set aside.
Heat the vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and season with salt and pepper. Cook for about 3-4 minutes until browned, then remove from the skillet and set aside.
In the same skillet, add the minced garlic and ginger. Stir-fry for about 30 seconds until fragrant.
Add the broccoli florets to the skillet and stir-fry for 2-3 minutes until they are bright green and tender-crisp.
Return the cooked beef to the skillet, then pour the sauce mixture over the beef and broccoli. Stir well to coat everything evenly. Cook for an additional 2-3 minutes until the sauce thickens.
Serve hot over cooked rice.