Bring a small pot of water to a boil, carefully lower the egg in, and cook for 6.5 minutes before transferring to an ice bath to peel.
In a separate medium saucepan, combine the chicken bone broth, grated ginger, and minced garlic, bringing the mixture to a gentle simmer.
Place the chicken breast into the simmering broth and poach until fully cooked through, approximately 10 to 12 minutes.
Remove the chicken from the pot, shred it using two forks, and set it aside.
Add the dry soba noodles to the broth and cook for 3 minutes.
Stir in the chopped bok choy, sriracha, and coconut aminos, continuing to cook for another 2 minutes until the noodles are tender.
Return the shredded chicken to the pot and stir in the lime juice, sea salt, and black pepper.
Pour the soup into a large bowl and top with the halved soft-boiled egg before serving.