Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and set aside.
Slice the chicken breast into thin, bite-sized strips and thinly shred the green cabbage and carrots.
Heat the toasted sesame oil in a large wok or skillet over medium-high heat.
Add the chicken strips to the skillet and cook until golden brown and cooked through, about 5-6 minutes.
Stir in the minced garlic, grated ginger, and red pepper flakes, cooking for 1 minute until fragrant.
Toss in the shredded cabbage, carrots, and sugar snap peas, sautéing for 3 minutes until the vegetables are tender-crisp.
Whisk together the tamari and water in a small bowl, then pour it over the chicken and vegetables.
Add the cooked soba noodles to the skillet and toss everything together until well-coated and heated through.
Garnish with thinly sliced green onions before serving.