Mix together the vinegar, honey, soy sauce and mirin in a small bowl.
Halve the cucumber lengthways and scoop out the seeds. Push the cucumber, fennel and radishes through a food processor fitted with a slicing attachment. (Alternatively, slice as thinly as possible by hand.)
Cut away any fat from the beef and slice very thinly. Dust with the cornflour.
Heat 2 tablespoons of the oil in a wok or large frying pan. Add the chilli, ginger and beef and stir-fry quickly for 1 minute. Drain to a large plate. Add the spring onions to the pan and stir-fry quickly for a further minute. Drain to the plate.
Heat a little more oil and stir-fry half the shredded vegetables for about 30 seconds. Drain to the plate. Stir-fry the remainder and drain to the plate.
Pour the remaining oil into the pan and add the noodles and coriander. Cook, stirring, for a few seconds to heat through and break up the noodles, then tip the beef and vegetables back into the pan. Add the vinegar mixture and cook for about 30 seconds until heated through. Serve immediately.