To prepare the beef, slice the flank steak against the grain and place it in a bowl. Add the salt and mix until the meat feels slightly tacky. Add the white pepper, soy sauce, dark soy sauce, Shaoxing wine, egg white, and cornstarch and mix thoroughly to coat. Add 1 tablespoon of cooking oil to seal in moisture and mix again. Let the beef marinate while preparing the remaining ingredients.
To prepare the vegetables, slice the onion, shallot, and scallions and set aside.
To cook the noodles, in a pot over high heat, bring water to a boil. Add the lo mein noodles and cook for about 3 minutes until just al dente. Rinse under cold water to stop the cooking, then drain well.
To make the stir-fry sauce, in a bowl, whisk together the soy sauce, dark soy sauce, oyster sauce, and chicken stock until combined.
To stir-fry the beef, in a wok over high heat, add 3 tablespoons of cooking oil. Add the beef and let it sear briefly before stirring. Stir-fry for about 3 minutes until cooked through. Remove and set aside.
To stir-fry the vegetables and noodles, in the same wok over high heat, add 1 tablespoon of cooking oil. Add the onion and shallot and stir-fry for about 30 seconds until fragrant. Add the noodles and stir-fry for about 1 minute until heated through and coated with the aromatics.
To combine everything, return the beef to the wok along with the stir-fry sauce. Add the scallions and bean sprouts and toss everything together until evenly combined and hot.