Cook soba 4–5 minutes, pull at al dente. Drain and rinse immediately under cold water, tossing well to remove starch. Shake off excess water.
Whisk all dressing ingredients together, adding water a little at a time until pourable but still thick. Taste and adjust.
Toss cooled noodles with edamame, carrot, and most of the scallions. Pour dressing over and toss to coat.
Rest 15 minutes, then toss again before portioning.
Divide into containers. Top with reserved scallions, peanuts, and sesame seeds. Store toppings separately for max crunch.