Bring a pot of water to a boil and cook the soba noodles according to package directions, then drain and set aside.
Slice the chicken breast into thin bite-sized strips and season evenly with the sea salt and black pepper.
Heat the avocado oil in a large skillet or wok over medium-high heat until shimmering.
Add the chicken to the skillet and sauté for 5-6 minutes until cooked through and lightly golden on the edges.
Add the shredded cabbage, matchstick carrots, minced garlic, and grated ginger to the pan, stir-frying for 3 minutes until the vegetables are tender-crisp.
Fold in the cooked soba noodles, tamari, and toasted sesame oil, tossing everything together for 2 minutes to meld the flavors.
Garnish the dish with thinly sliced green onions and serve immediately while hot.