Cook the soba noodles according to the package instructions. Drain and rinse under cold water to stop the cooking process and cool the noodles.
In a small bowl or mason jar, combine all the dressing ingredients and whisk or shake until well combined.
In a large bowl, combine the cooked soba noodles, green cabbage, purple cabbage, carrots, snap peas, cilantro, green onions, and sesame seeds. Pour the dressing over the salad and toss until everything is evenly coated.