In a small bowl, whisk together soy sauce, oyster sauce, cornstarch, and water until smooth. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat.
Add the sliced beef to the skillet and season with black pepper. Stir-fry for 3-4 minutes until browned and just cooked through. Remove beef from the skillet and set aside.
Add the remaining 1 tablespoon of vegetable oil to the skillet.
Add minced garlic and ginger, stir-fry for 30 seconds until fragrant.
Add red bell pepper, green bell pepper, carrot, and broccoli florets. Stir-fry for 4-5 minutes until vegetables are tender-crisp.
Return the cooked beef to the skillet with the vegetables.
Pour the sauce mixture over the beef and vegetables, stirring constantly until the sauce thickens and coats everything, about 2 minutes.
Drizzle sesame oil over the stir fry and toss to combine.
Remove from heat and garnish with sliced green onions.
Serve immediately with steamed rice or noodles.