In a bowl, combine the soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and sugar. Whisk until smooth and set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and season with salt and pepper. Stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the minced garlic and ginger, and 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 beef to the skillet and pour the sauce mixture over the beef and broccoli. Stir well to combine and cook for an additional 2-3 minutes until the sauce thickens.
Serve hot over cooked rice.