Heat a wok with 1 tbsp oil over high heat. Stir-fry the lamb mince, in 2 batches, until browned. Set mince aside.
Reheat the wok over medium-high heat, add the remaining oil, and add the garlic, ginger, onion and celery. Stir-fry for 1 minute. Add the water chestnuts, corn, snow peas, and Chinese broccoli, and stir-fry for 30 seconds.
Return the mince to the wok, toss for 1 minute. Pour in the combined plum sauce, soy sauce and 2 tbsp water, stirring as it comes to the boil.
Meanwhile, cook the noodles according to packet instructions. Drain and drizzle noodles with the sesame oil.
Serve the mince with the noodles, topped with green onions and sesame seeds, and Japanese mayonnaise, if desired.