In a medium bowl, whisk together soy sauce, oyster sauce, chili garlic sauce, brown sugar, cornstarch, and water until smooth. Set the sauce mixture aside.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced beef to the skillet in a single layer and cook for 2-3 minutes without stirring to sear, then stir and cook for another 1-2 minutes until beef is browned but not fully cooked. Remove beef from skillet and set aside.
In the same skillet, add the remaining 1 tablespoon vegetable oil.
Add minced garlic and ginger and stir-fry for 30 seconds until fragrant.
Add broccoli florets and stir-fry for 3-4 minutes until they are bright green and crisp-tender.
Return the beef to the skillet with the broccoli.
Stir the prepared sauce mixture once more and pour it into the skillet.
Cook, stirring constantly, for 2-3 minutes until the sauce thickens and coats the beef and broccoli evenly.
Stir in toasted sesame oil and crushed red pepper flakes.
Remove from heat and garnish with sliced green onions.
Serve immediately over steamed rice or noodles if desired.