Bring a medium pot of water to a boil and cook the buckwheat soba noodles for 4-5 minutes until tender, then drain and rinse immediately with cold water to prevent sticking.
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 or wok over medium-high heat.
Add the chicken to the skillet and sauté for 6-8 minutes until golden brown and cooked through, then remove the chicken and set aside.
In the same skillet, add the broccoli florets and sliced red bell pepper with a tablespoon of water; cover and steam for 2-3 minutes until vibrant and crisp-tender.
While the vegetables cook, whisk together the tamari, honey, grated fresh ginger, and minced garlic in a small bowl.
Return the chicken and the cooked soba noodles to the skillet with the vegetables.
Pour the tamari mixture over the ingredients and toss constantly for 1-2 minutes until the sauce thickens and evenly glazes the stir-fry.
Transfer to a plate and garnish with sesame seeds before serving.