Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the sliced flank steak and cook for about 3-4 minutes until browned. Remove the steak from the skillet and set aside.
In the same skillet, add the remaining tablespoon of vegetable oil. Add the sliced onion and bell peppers. Stir-fry for about 5 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger, and cook for an additional 1 minute until fragrant.
In a small bowl, mix together the soy sauce, oyster sauce, cornstarch, beef broth, black pepper, and sesame oil. Pour this sauce over the vegetables in the skillet and stir well.
Return the cooked steak to the skillet and toss everything together. Cook for another 2-3 minutes until the sauce thickens and everything is heated through.
Serve the pepper steak over cooked rice.