In a large bowl, combine the sliced steak and shrimp. Season with salt and pepper, and set aside.
In a large skillet or wok, heat 1 tablespoon of vegetable oil over medium-high heat. Add the steak and cook for 2-3 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 bell peppers and snap peas, and stir-fry for about 3-4 minutes until they are tender-crisp.
Add the minced garlic and ginger to the vegetables, stirring for about 30 seconds until fragrant.
Return the steak to the skillet along with the shrimp. Cook for an additional 2-3 minutes until the shrimp are pink and cooked through.
In a small bowl, mix the soy sauce, oyster sauce, cornstarch, and water. Pour this sauce over the stir-fry and toss everything together until well coated. Drizzle with sesame oil before serving.
Serve hot over cooked rice or noodles.