Bring a small pot of water to a boil, carefully lower the egg into the water, and cook for 6 minutes and 30 seconds before transferring to an ice bath.
Season the chicken breast with sea salt and black pepper on both sides.
Heat toasted sesame oil in a medium pot over medium-high heat and sear the chicken until golden and cooked through, about 5-6 minutes per side.
Remove the chicken from the pot, let it rest for a few minutes, then slice it into thin strips.
In the same pot, add the minced garlic, ginger, and sliced shiitake mushrooms, sautéing for 2 minutes until fragrant.
Stir in the gochujang and tamari, then pour in the chicken broth and bring the mixture to a gentle simmer.
Add the dry soba noodles and chopped baby bok choy to the simmering broth, cooking for 4-5 minutes until the noodles are tender.
Peel the soft-boiled egg and slice it in half lengthwise.
Pour the broth, noodles, and vegetables into a large bowl, then top with the sliced chicken and the egg halves.