To make the dressing, whisk to combine the soy sauce, rice vinegar, mirin, sriracha, sesame oil, ginger, and sesame seeds. Set aside.
Bring a big pot of water to a boil and season the water with enough salt for it to taste like ocean water. Cook the soba noodles according to the time on the package, checking a few minutes before to see if the soba noodles are done.
When the soba noodles are al dente, immediately drain the noodles. Depending on how cold you want the noodles, either rinse the noodles with cold running water for 1 minute, or place them in a big bowl of ice water to chill, for about 30 seconds. Drain the noodles and transfer to a bowl.
Toss the soba noodles with the Asian dressing and mix with the grated cucumber, scallions, and chicken breast. It is best to eat either at room temperature or after it has chilled in the fridge. The noodles are best eaten within a day or two. Enjoy!