Bring a small pot of water to a boil and cook the egg for 6.5 minutes, then immediately transfer to an ice bath to cool.
In a medium pot, heat the toasted sesame oil over medium heat and sauté the minced garlic and grated ginger for 1 minute until fragrant.
Pour in the chicken broth, tamari, and sriracha, bringing the mixture to a gentle simmer.
Season the chicken breast with sea salt and black pepper, slice it into thin strips, and add it to the simmering broth.
Cook the chicken for 4-5 minutes until fully opaque and tender.
While the chicken cooks, prepare the soba noodles in a separate pot according to package directions, then drain.
Add the chopped bok choy to the broth during the last 2 minutes of cooking until the leaves are wilted and the stems are tender-crisp.
Place the cooked soba noodles in a large bowl, pour the broth, chicken, and bok choy over them, and top with the peeled and halved soft-boiled egg and sliced green onions.