Prepare the miso sauce by softening the miso paste in the hot water. Whisk until smooth, then whisk in the lime juice and rice wine vinegar, and set to one side.
Blanch the asparagus in a large saucepan of boiling, salted water for 1 minute. Drain and toss with half of the sesame oil.
Reheat the noodles if necessary and toss with the rest of the sesame oil to coat evenly. Add the miso sauce and toss well again to coat. Spoon into serving bowls and serve the asparagus alongside.