In a small bowl, whisk together soy sauce, brown sugar, oyster sauce, sesame oil, garlic, and ginger.
In another bowl, mix cornstarch with water or beef broth to create a slurry.
Place the thinly sliced beef in a bowl and pour half of the soy sauce mixture over it. Let it marinate for at least 15 minutes.
Heat your flat-top griddle to medium-high heat.
Lightly oil the griddle.
Cook the marinated beef in a single layer, allowing it to sear and brown. This should take about 2-3 minutes per side.
Once the beef is cooked and has a nice sear, remove it from the griddle and set it aside.
Add a bit more oil to the griddle if needed.
Add the broccoli florets and stir-fry until they are bright green and tender-crisp, about 3-4 minutes.
Return the cooked beef to the griddle with the broccoli.
Pour the remaining soy sauce mixture and the cornstarch slurry over the beef and broccoli.
Stir everything together and cook for an additional 1-2 minutes, or until the sauce has thickened and coats the beef and broccoli evenly.
Garnish with chopped green onions.
Serve hot, ideally over a bed of steamed rice or noodles.