Bring a small pot of water to a boil and carefully lower in the egg, cooking for exactly 6 minutes and 30 seconds before transferring to an ice bath.
Cook the soba noodles in a separate pot of boiling water according to package directions, then drain and set aside.
In a medium saucepan, heat the sesame oil over medium-high heat and sauté the diced chicken breast until golden and cooked through.
Add the minced garlic, grated ginger, and sliced shiitake mushrooms to the pan, stirring for 2 minutes until fragrant.
Pour in the chicken broth, sriracha, tamari, sea salt, and black pepper, bringing the liquid to a gentle simmer.
Stir in the chopped bok choy and cook for 1-2 minutes until the greens are wilted but the stems remain crisp.
Place the cooked soba noodles in a deep bowl and pour the hot soup and chicken mixture over them.
Peel the cooled egg, slice it in half to reveal the jammy yolk, and place it on top of the noodles before serving.