Bring a large pot of water to a boil. Salt the water, add the noodles and cook until almost al dente. Add the celery, carrots and bean sprouts to the pot. Cook until the vegetables soften slightly, 30 to 60 seconds. Drain; rinse with cold water and drain well. Transfer to a large bowl and toss with the sesame oil.
In a medium bowl, whisk the tahini, soy sauce, chili oil, balsamic vinegar, cider vinegar and sugar. Season with salt. Pour over the noodles. Add the scallions and toss to coat.