Cook the dried stir-fry noodles or thin egg noodles according to the package instructions until just tender. Drain well, rinse briefly with cool water to stop the cooking, and set aside.
Place the thinly sliced flank steak in a small bowl. Add the cornstarch, 1 tablespoon of soy sauce, and black pepper. Toss until the steak is evenly coated and let it sit while you prepare the other ingredients.
In a separate small bowl, whisk together the remaining 1 tablespoon of soy sauce, oyster sauce, hoisin sauce, sesame oil, and water to make the stir-fry sauce. Set aside.
Heat 1 tablespoon of vegetable oil in a large skillet or wok over medium-high heat. Add the marinated steak in a single layer and cook for 2 to 3 minutes, stirring occasionally, until browned and just cooked through. Transfer the steak to a plate.
In the same skillet, add the shrimp. Cook for 2 to 3 minutes, stirring, until the shrimp are pink and opaque. Transfer the shrimp to the plate with the steak.
Add the remaining 1 tablespoon of vegetable oil to the skillet. Add the minced garlic and minced ginger and cook for about 30 seconds, stirring constantly, until fragrant but not browned.
Add the broccoli florets, carrot matchsticks, and red bell pepper slices to the skillet. Stir-fry for 3 to 4 minutes until the vegetables are crisp-tender.
Return the cooked noodles to the skillet with the vegetables. Pour the stir-fry sauce over the noodles and toss well to coat everything evenly.
Add the cooked steak and shrimp back into the skillet. Toss gently for 1 to 2 minutes over medium heat until everything is heated through and the sauce lightly coats the noodles, steak, shrimp, and vegetables.
Taste and adjust seasoning if needed, then remove from the heat. Serve the Steak and Shrimp Stir-Fry Noodles hot.