Bring a small pot of water to a boil, add the egg, and cook for exactly 6.5 minutes for a jammy yolk, then immediately transfer to an ice bath.
In a medium pot, heat the toasted sesame oil over medium heat and sauté the diced chicken breast until golden brown and cooked through.
Add the minced garlic, grated ginger, and sliced mushrooms to the pot, stirring for 2 minutes until the vegetables are fragrant.
Pour in the chicken broth, tamari, and sriracha, bringing the mixture to a gentle simmer over medium-high heat.
Add the soba noodles and cook for 4-5 minutes until tender, tossing in the chopped bok choy during the last minute of cooking to wilt.
Season the broth with sea salt and black pepper, then pour into a deep bowl and top with the peeled and halved soft-boiled egg.