In a bowl, combine the sliced flank steak, soy sauce, and cornstarch. Mix well and let it 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 sliced onion and bell pepper, and stir-fry for 2-3 minutes until they start to soften.
Add the minced garlic and broccoli florets to the skillet. Stir-fry for another 2-3 minutes until the broccoli is bright green and tender-crisp.
Return the beef to the skillet. Add the oyster sauce and sesame oil, stirring to combine. Cook for an additional 2 minutes, allowing the flavors to meld. Season with salt and pepper to taste.
Serve the stir-fry over cooked rice.