In a bowl, combine the soy sauce, brown sugar, water and garlic. Add the sliced beef and mix well to coat. Marinate for 10–20 minutes.
Cook the egg noodles according to the packet instructions. Drain and set aside.
Heat the oil in a wok or large frying pan over high heat. Remove the beef strips from the marinade, reserving the marinade for the sauce.
Stir-fry the beef in batches for 1–2 minutes, or until just browned. Remove from the pan and set aside.
In the same pan, stir-fry the carrot, red onion and mixed vegetables for 2–3 minutes. Add 2 Tbsp water, cover briefly and allow the vegetables to steam until just tender.
Return the beef to the pan. Add the reserved marinade and cornflour and cook for 1–2 minutes, stirring, until the sauce thickens and becomes glossy. Stir through the cashews.
Add the cooked noodles and vegetables and toss everything together until evenly coated and heated through.
Sprinkle with sesame seeds and serve immediately.