Place a large saucepan of water over high heat and bring to a boil.
Add the salt and stir to dissolve. Add the egg noodles, stir well, and cook according to package instructions.
Drain noodles in a colander, rinse under cool running water. tossing until all excess liquid has been removed. Transfer to a large bowl and toss with sesame oil; set aside.
To a medium bowl, add soy sauce, hoisin, and wine; whisk to combine. Add beef, toss to coat, and set aside.
Heat a wok over high heat until beginning to smoke. Add 1 tablespoon peanut oil and swirl to coat.
Add onion and cook, stirring and tossing occasionally, until slightly browned, 2 to 3 minutes. Add the broccoli and red bell pepper and cook, stirring and tossing occasionally, until the broccoli is barely tender, 3 to 4 minutes.
Add the garlic, ginger and green onion and cook for 1 minute, stirring constantly. Transfer the vegetables to the bowl with the noodles.
Return the wok to high heat until beginning to smoke. Add the remaining 1 tablespoon peanut oil and swirl to coat the sides.
Drain the beef, reserving the marinade and add the meat to the wok. Cook, stirring and tossing for 2 minutes. Add the reserved sauce, broth, vinegar and stir.
Add the reserved noodles and vegetables. Toss until the noodles are coated and vegetables are heated through.
To serve: transfer to a serving dish, drizzle lightly with sesame oil, garnish with green onions and serve family style.