In a bowl, combine the sliced flank steak with 2 tablespoons of soy sauce, 1 tablespoon of cornstarch, and 1 tablespoon of sesame oil. Marinate for at least 15 minutes.
In a separate small bowl, whisk together all the sauce ingredients: beef broth, 0.25 cup soy sauce, oyster sauce, brown sugar, and 1 tablespoon cornstarch. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef in a single layer and sear for 1-2 minutes per side until browned. Remove beef from skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add minced garlic and grated ginger, and stir-fry until fragrant, about 30 seconds.
Add the broccoli florets to the skillet and stir-fry for 3-4 minutes until tender-crisp. You can add a tablespoon or two of water if needed to steam the broccoli.
Pour the prepared sauce mixture into the skillet. Bring to a simmer, stirring constantly, until the sauce thickens.
Return the seared beef to the skillet and toss to coat with the sauce. Cook for another 1-2 minutes until the beef is heated through.
Serve hot, typically over steamed rice.
Notes
For a spicier kick, add a pinch of red pepper flakes with the garlic and ginger. You can also add other vegetables like bell peppers or snap peas.