In a small bowl, whisk together soy sauce, oyster sauce, brown sugar, cornstarch, beef broth, sesame oil, black pepper, and crushed red pepper flakes (if using). Set the sauce mixture aside.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat.
Add the thinly sliced flank steak to the skillet in a single layer. Cook for about 2-3 minutes on each side until browned but not fully cooked through. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining 1 tablespoon of vegetable oil.
Add the minced garlic and sauté for 30 seconds until fragrant.
Add the broccoli florets and stir-fry for 4-5 minutes, until they are bright green and just tender but still crisp.
Return the beef to the skillet with the broccoli.
Pour the prepared sauce over the beef and broccoli, stirring to coat everything evenly.
Cook for an additional 2-3 minutes, stirring frequently, until the sauce thickens and the beef is cooked through.
Remove from heat and garnish with sliced green onions.
Serve immediately over steamed rice or noodles if desired.