Bring a medium pot of water to a boil and cook the soba noodles according to package directions, then drain and rinse with cold water.
While noodles cook, whisk together the tamari, honey, rice vinegar, and grated fresh ginger in a small bowl to create the sauce.
Cut the chicken breast into bite-sized pieces and season with sea salt and black pepper.
Heat the toasted sesame oil in a large skillet over medium-high heat. Add the chicken and sear until golden and cooked through, about 5-6 minutes.
Add the minced garlic, broccoli florets, and shredded carrots to the skillet, sautéing for 3 minutes until the vegetables are crisp-tender.
Lower the heat to medium and add the cooked soba noodles and the prepared sauce to the skillet.
Toss everything together for 1-2 minutes until the noodles are well-coated and the sauce has slightly thickened.
Serve immediately, garnished with sliced green onions and toasted sesame seeds.