In a large bowl, combine the sliced steak and shrimp. Season with salt and pepper, then set aside.
In a small bowl, mix together soy sauce, oyster sauce, cornstarch, and water. Set this sauce mixture aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the steak and stir-fry for about 2-3 minutes until browned. Remove the steak from the skillet and set aside.
In the same skillet, add the remaining tablespoon of oil. Add the bell pepper, onion, and broccoli. Stir-fry for 3-4 minutes until the vegetables are tender-crisp.
Add the minced garlic and ginger to the vegetables, stirring for about 30 seconds until fragrant.
Return the cooked steak to the skillet, then add the shrimp. Pour the sauce mixture over the stir-fry and cook for an additional 2-3 minutes until the shrimp are pink and cooked through.
Drizzle with sesame oil before serving. Serve hot over cooked rice or noodles.