Slice the flank steak against the grain into thin strips.
In a mixing bowl, combine 3 tablespoons of cornstarch with 3 tablespoons of water. Stir until smooth, then add the sliced beef, ensuring each piece is well coated. Let it marinate while you prepare the other ingredients.
In a separate bowl, mix together the grated ginger, soy sauce, sesame oil, ground black pepper, brown sugar, and minced garlic.
In a wok or large skillet, heat 1 tablespoon of vegetable oil over medium-high heat. Add the broccoli florets, stirring frequently for about 3-4 minutes until they become bright green and tender-crisp. Remove the broccoli from the pan and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Once hot, add the marinated beef strips, spreading them in a single layer. Allow them to sear for 2-3 minutes without stirring, then stir-fry until fully cooked, about another 2-3 minutes.
Return the cooked broccoli to the skillet with the beef. Pour the sauce over the mixture, stirring well to coat everything evenly. Cook for an additional minute until the sauce thickens slightly.
Serve the Easy Beef and Broccoli hot over cooked white rice and sprinkle with sesame seeds for a finishing touch.