In a medium bowl, combine the soy sauce, oyster sauce, chili garlic sauce, cornstarch, water, brown sugar, and sesame oil. Stir well until the cornstarch is fully dissolved and set aside.
Heat 2 tablespoons of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced beef to the skillet and stir-fry for 3 to 4 minutes until browned and just 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 ginger and stir-fry for 30 seconds until fragrant.
Add the broccoli florets and stir-fry for 4 to 5 minutes until they are bright green and tender-crisp.
Return the cooked beef to the skillet with the broccoli.
Pour the prepared sauce over the beef and broccoli mixture.
Add the crushed red pepper flakes and stir everything together.
Cook for an additional 2 minutes, stirring constantly, until the sauce thickens and coats the beef and broccoli evenly.
Remove from heat and garnish with sliced green onions before serving.