Boil water and cook soba noodles according to package instructions, then drain and set aside.
Cut the chicken breast into 1-inch cubes and toss in a bowl with arrowroot powder, sea salt, and black pepper until evenly coated.
In a small jar, whisk together the coconut aminos, honey, and rice vinegar to create the stir-fry sauce.
Heat the toasted sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and sear for 5-6 minutes until golden brown and crispy on all sides.
Stir in the sliced red bell pepper, snap peas, minced ginger, and minced garlic, sautéing for 3 minutes until the vegetables are tender-crisp.
Pour the sauce over the chicken and vegetables, tossing constantly for 1 minute until the glaze thickens and becomes glossy.
Add the cooked soba noodles to the pan, tossing gently to combine and warm through before serving.