In a large bowl, combine the sliced steak and shrimp. Season with salt and pepper, then set aside.
In a small bowl, whisk 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 cook 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 vegetable oil. Add the garlic and ginger, sautéing for about 30 seconds until fragrant.
Add the bell peppers, broccoli, and snap peas to the skillet. Stir-fry for about 3-4 minutes until the vegetables are tender-crisp.
Return the cooked steak to the skillet, followed by the shrimp. Pour the sauce mixture over the stir-fry and cook for an additional 2-3 minutes, stirring frequently, until the shrimp are pink and cooked through.
Drizzle with sesame oil before serving. Serve hot over cooked rice or noodles.