Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and 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 and stir-fry for another 3-4 minutes until they are bright green and tender-crisp.
In a small bowl, whisk together the soy sauce, oyster sauce, cornstarch, beef broth, sesame oil, and sugar. Pour this sauce over the broccoli and stir well to combine.
Return the beef to the skillet and cook for an additional 2-3 minutes, stirring frequently, until the sauce thickens and everything is heated through.
Serve the beef and broccoli stir-fry over cooked rice.