Bring a pot of salted water to a boil; add the chow mein noodles and cook according to package instructions.
Preheat the oil in a large pan over medium high heat.
Add the steak in a single layer. Cook for 3-4 minutes per side or until browned.
Remove the steak from the pan and cover to keep warm. Add the onions, carrots and celery to the pan and cook for 3-4 minutes or until just softened. Season with salt and pepper to taste.
Add the garlic and cook for 30 seconds.
Add the beef, noodles and cabbage to the pan. Toss to combine.
In a small bowl, whisk together the soy sauce, sugar, beef broth, cornstarch and sesame oil. Add the sauce to the pan. Bring to a simmer and cook for 1 minute.
Stir until sauce evenly coats the noodles. Add the green onion tops and cook for 1-2 more minutes, until green onions and cabbage are wilted. Serve immediately.