Stir fry the onion and carrot for 3-4 minutes until they begin to soften. Then add the mushrooms, cabbage, and green onions, and continue stir frying for an additional 2-3 minutes.
Return the beef to the wok along with the drained noodles. Pour in the prepared sauce and toss everything together over medium-high heat for about 2 minutes until well combined and heated through.