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 for easy peeling.
Cook the dry soba noodles in a separate pot of boiling water according to package directions, then drain and rinse with cold water to prevent sticking.
In a large pot, heat the toasted sesame oil over medium-high heat and brown the ground pork with sea salt and black pepper until fully cooked.
Add the minced garlic, grated ginger, and sliced shiitake mushrooms to the pot, sautéing for 3 minutes until the mushrooms are softened and fragrant.
Pour in the chicken broth, tamari, and sriracha, bringing the liquid to a gentle simmer to meld the spicy flavors.
Stir in the chopped bok choy and cook for 2 minutes until the leaves are just wilted but the stalks remain crisp.
Place the cooked soba noodles into a deep bowl, ladle the spicy pork and broth over them, and garnish with the halved soft-boiled egg and sliced green onions.