Bring a pot of water to a boil and cook the soba noodles for 4-5 minutes until tender, then drain and rinse with cold water.
Slice the chicken breast into thin strips and season with the sea salt and black pepper.
Heat one teaspoon of toasted sesame oil in a large skillet or wok over medium-high heat.
Add the chicken to the skillet and sauté until golden brown and cooked through, about 5-6 minutes, then remove and set aside.
In the same skillet, add the remaining teaspoon of sesame oil along with the shiitake mushrooms.
Cook the mushrooms undisturbed for 2-3 minutes to achieve a deep char, then stir and cook for another 2 minutes.
Add the baby bok choy, minced ginger, and minced garlic to the skillet, sautéing for 2 minutes until the greens are wilted but stems remain crisp.
Return the chicken to the skillet and add the cooked soba noodles and tamari.
Toss everything together for 1 minute until well combined and heated through before serving.