Bring a pot of water to a boil and cook the soba noodles for 5-6 minutes until tender, then drain and rinse with cold water.
In a small bowl, whisk together the honey, tamari, minced garlic, grated ginger, and arrowroot powder to create the glaze.
Pat the diced chicken breast dry with a paper towel and season evenly with sea salt and black pepper.
Heat the sesame oil in a large non-stick skillet over medium-high heat and sear the chicken until golden brown and cooked through.
Add the broccoli florets and sliced red bell pepper to the skillet, sautéing for 3-4 minutes until they reach a tender-crisp texture.
Pour the honey-garlic sauce into the skillet and stir constantly for 1 minute until the glaze becomes thick and glossy.
Add the cooked soba noodles to the pan, tossing everything together until well-coated and heated through.