In a medium bowl, combine the sliced beef, soy sauce, oyster sauce, and cornstarch. Mix well and let marinate for 10 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the marinated beef to the skillet and stir-fry for 3-4 minutes until the beef is browned and cooked through. Remove the beef from the skillet and set aside.
In the same skillet, heat the remaining 1 tablespoon of vegetable oil.
Add the minced garlic and ginger, and stir-fry for 30 seconds until fragrant.
Add the sliced onion, red bell pepper, green bell pepper, broccoli florets, and julienned carrot to the skillet. Stir-fry the vegetables for 4-5 minutes until they are tender-crisp.
Return the cooked beef to the skillet with the vegetables.
Pour in the beef broth and drizzle the sesame oil over the mixture. Stir well to combine.
Cook for an additional 2 minutes, allowing the sauce to thicken slightly and coat the beef and vegetables.
Season with black pepper to taste.
Remove from heat and garnish with sliced green onions before serving.