In a bowl, combine the sliced beef, soy sauce, oyster sauce, and cornstarch. Mix well and let marinate for at least 15 minutes.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated beef and stir-fry for about 3-4 minutes until browned. Remove the beef from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the garlic and ginger, and sauté for about 30 seconds until fragrant.
Add the sliced bell peppers and broccoli florets to the skillet. Stir-fry for about 4-5 minutes until the vegetables are tender-crisp.
Return the beef to the skillet and add the green onions and sesame oil. Stir everything together and cook for an additional 2 minutes. Season with salt and pepper to taste.
Serve the stir fry over cooked rice or noodles.