Wrap the beef fillet in clingfilm and place in the freezer for about 1 hour until it is semi-frozen. Remove and use a sharp knife to slice very thinly, against the grain.
Whisk together the soy sauce, mirin, sake and sugar in a small bowl to make a sauce.
Cook the noodles in a large saucepan of boiling water for 6–8 minutes, or according to the packet instructions, until tender.
Meanwhile, heat a wok or large frying pan until smoking hot, add the sesame oil and onions and stir-fry for 2–3 minutes. Add the shiitake or chestnut mushrooms and the bean sprouts or enoki mushrooms and stir-fry for a further 2–3 minutes or until softened. Stir in the beef and fry for 2 minutes, then pour in the prepared sauce and bubble for 1 minute.
Drain the noodles and heap into deep bowls, then spoon over the beef, pouring over any sauce left in the wok. Sprinkle with the spring onion and sesame seeds and serve immediately.