Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and rinse with cold water to stop the cooking.
Season the chicken breast with a pinch of sea salt and poach in simmering water for 12 to 15 minutes until cooked through, then shred with two forks.
In a small bowl, whisk together the tamari, rice vinegar, sesame oil, grated ginger, and minced garlic to create the dressing.
In a large mixing bowl, combine the chilled noodles, shredded chicken, shredded cabbage, julienned carrots, and sliced cucumber.
Pour the ginger-sesame dressing over the salad and toss thoroughly to ensure every ingredient is well-coated.
Garnish the salad with sliced green onions and toasted sesame seeds before serving.