In a medium pot, bring the chicken broth, minced garlic, and grated ginger to a gentle simmer over medium heat.
Place the chicken breast into the broth and poach for 12 to 15 minutes until fully cooked, then remove and shred with two forks.
While the chicken poaches, cook the soba noodles in a separate pot of boiling water according to the package instructions, then drain and set aside.
Add the sliced shiitake mushrooms and chopped bok choy to the simmering broth and cook for 3 minutes until the vegetables are tender.
Stir in the tamari, sesame oil, sea salt, and black pepper to the broth to finalize the base.
Place the cooked soba noodles in a large bowl, top with the shredded chicken, and pour the hot broth and vegetables over the top.
Garnish with thinly sliced green onions and serve immediately.