Prepare the beef and broccoli: Thinly slice the flank steak against the grain and cut the broccoli into bite-sized florets.
Make the sauce: In a small bowl, whisk together the soy sauce, oyster sauce, beef broth, cornstarch, brown sugar, sesame oil, and red pepper flakes (if using). Set aside.
Cook the broccoli: In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat. Add the broccoli and stir-fry for 3-4 minutes until bright green and slightly tender. Remove the broccoli from the skillet and set aside.
Cook the beef: In the same skillet, heat the remaining 2 tablespoons of vegetable oil over high heat. Add the sliced beef in a single layer and cook for 2-3 minutes, until browned. Stir in the minced garlic and grated ginger, and cook for an additional minute.
Combine and finish: Return the cooked broccoli to the skillet. Pour in the prepared sauce and stir to combine. Cook for 2-3 minutes, or until the sauce thickens and coats the beef and broccoli evenly.
Serve: Remove from heat and serve immediately over cooked white rice. Garnish with sesame seeds and sliced green onions.