In a bowl, combine sliced beef with 1 tablespoon soy sauce and 1 tablespoon cornstarch; marinate for 15 minutes.
In a small bowl, whisk together beef broth, oyster sauce, brown sugar, sesame oil, and the remaining 1 tablespoon soy sauce to create the sauce.
Blanch broccoli florets in boiling water for 2 minutes, then drain and set aside.
Heat 1 tablespoon oil in a wok or large skillet over high heat until smoking.
Sear the beef in batches until browned on both sides; remove and set aside.
Add the remaining 1 tablespoon oil to the wok; stir-fry minced garlic and ginger for 30 seconds until fragrant.
Add the blanched broccoli and seared beef back into the wok.
Pour the prepared sauce over the ingredients and toss continuously until the sauce thickens and coats the beef and broccoli.
Serve immediately.