Cook the dried egg noodles according to the package instructions in a large pot of boiling water until just tender. Drain well and set aside.
In a small bowl, whisk together the soy sauce, oyster sauce, hoisin sauce, brown sugar, cornstarch, water, and sesame oil until smooth with no cornstarch lumps. Set this sticky sauce mixture aside.
Pat the thinly sliced beef steak dry with paper towels and season with the black pepper and half of the salt, tossing to coat the slices evenly.
Heat 1 tablespoon of the vegetable oil in a large frying pan or wok over medium-high heat. Add the seasoned beef in a single layer and cook for 3 to 4 minutes, stirring occasionally, until just browned and no longer pink. Transfer the beef to a plate and keep warm.
In the same pan, add the remaining 1 tablespoon of vegetable oil. Add the sliced onion and the white parts of the spring onions and cook for 2 to 3 minutes until starting to soften.
Add the chopped garlic, carrot matchsticks, and sliced red bell pepper to the pan. Cook for another 3 to 4 minutes, stirring, until the vegetables are slightly tender but still bright in colour.
Give the prepared sticky sauce mixture a quick stir, then pour it into the pan with the vegetables. Stir well and let it simmer for 2 to 3 minutes until it starts to thicken and turn glossy.
Return the cooked beef and any resting juices to the pan. Toss everything together so the beef is well coated in the sticky sauce, and simmer for 1 to 2 minutes more. Taste and add the remaining salt if needed.
Add the drained cooked noodles to the pan. Using tongs, gently toss the noodles with the sticky beef and vegetables until everything is evenly coated and heated through, about 2 minutes.
Remove the pan from the heat and sprinkle over the green parts of the sliced spring onions. Serve the sticky beef noodles hot in bowls.