Bring a small pot of water to a boil, carefully lower the egg into the water, and simmer for exactly 6 minutes and 30 seconds.
Immediately transfer the egg to an ice bath, then peel and slice in half once cooled.
In a large pot, heat the sesame oil over medium heat and sauté the diced chicken breast until golden brown.
Stir in the grated ginger and minced garlic, cooking for 1 minute until fragrant.
Pour in the chicken broth, tamari, and sriracha, bringing the liquid to a gentle simmer.
Add the sliced shiitake mushrooms and brown rice ramen noodles, cooking for 4 minutes until the noodles are tender.
Add the chopped bok choy during the last minute of cooking to wilt it slightly while keeping a crunch.
Season with sea salt and black pepper, then ladle the soup into a bowl.
Top with the soft-boiled egg halves and sliced green onions before serving.