How to Make It
In a small saucepan, combine the shiitake with the soy sauce, mirin and ginger and simmer over low heat for 10 minutes. Strain the liquid into a blender and add the sweet chile sauce and oil. Blend until emulsified. Let the dressing cool.
Meanwhile, bring a large pot of lightly salted water to a boil and fill a large bowl with ice water. Boil the soba noodles until tender, 3 minutes. Drain in a colander and set the colander in the ice water. Toss the noodles to cool; drain well, shaking out the excess water, and transfer to a bowl. Add the carrots, daikon, bean sprouts, sesame seeds and dressing to the noodles and toss to coat. Serve lightly chilled or at room temperature.
Pickled daikon radishes are available at Japanese and Korean markets. Any pickled radish is a good substitute.