Cook the noodles for 6-8 minutes, or according to package directions.
Drain and toss with just a drizzle of cooking oil to keep them from sticking together.
Put in the refrigerator to cool.
Peel the carrots and shave with a peeler or mandolin. You should have about 2-3 cups of loose carrot shavings.
Chop the green parts of the scallions and set the white parts aside for another recipe.
Whisk the sesame oil, vinegar, and soy sauce together and taste. Adjust for taste.
Toss the carrots, scallions, chilled noodles and sesame seeds together and serve.