Bring a small pot of water to a boil and cook the egg for 6.5 minutes, then immediately transfer to an ice bath.
In a separate pot, cook the soba noodles according to package directions, then drain and set aside.
Season the chicken breast with a pinch of salt and sear in a pan over medium heat until cooked through, then slice thinly.
In a medium saucepan, combine chicken broth, tamari, grated ginger, and minced garlic; bring to a gentle simmer.
Add sliced shiitake mushrooms and baby bok choy to the broth, simmering for 3 minutes until the greens are vibrant.
Peel and halve the soft-boiled egg.
Place noodles in a deep bowl, pour the hot broth and vegetables over them, and top with the sliced chicken.
Finish the bowl with the egg halves, a drizzle of sesame oil, sliced green onions, and toasted sesame seeds.