Cook the soba noodles according to the package instructions.
While the soba noodles are cooking, make the dressing. Whisk together all the ingredients (minus water) until combined. The mixture will be thick, so whisk in some water, about 1 tablespoon at a time, until you reach a consistency that is pourable.
Once the noodles are done, drain them in a colander and rinse them under cold water, using your hands to separate the noodles. Continue to rinse until the noodles are cool and not sticky.
Place the noodles in a large bowl. Add the vegetables and edamame, then pour the dressing over top. Toss together with salad tongs.
Serve immediately or store in the fridge for 2 - 3 days.