Bring a pot of water to boil and cook the soba noodles according to package directions, then drain and rinse with cold water.
Slice the chicken breast into bite-sized strips and season with sea salt and black pepper.
In a small bowl, whisk together the hoisin sauce, tamari, and toasted sesame oil until smooth.
Heat the avocado oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and sear until golden brown and cooked through, about 5-6 minutes.
Remove the chicken from the pan and set aside.
In the same skillet, add the broccoli florets and sliced red bell pepper, stir-frying for 3-4 minutes until tender-crisp.
Add the minced garlic and grated ginger to the vegetables, sautéing for 30 seconds until fragrant.
Return the chicken to the skillet and pour the hoisin sauce mixture over the top.
Toss everything together for 1 minute until the sauce thickens and coats the chicken and vegetables evenly.
Serve the hoisin chicken and vegetables over the cooked soba noodles.