Bring a small pot of water to a boil, carefully lower the egg into the water, and simmer for 6 minutes and 30 seconds for a jammy yolk.
Remove the egg and place it in an ice bath immediately; once cooled, peel and slice it in half.
Cook the soba noodles according to package directions, then drain and rinse under cold water to prevent sticking.
In a medium saucepan, heat the sesame oil over medium heat and brown the ground pork until cooked through, seasoning with sea salt.
Add the minced garlic, grated ginger, and sliced shiitake mushrooms to the pork, sautéing for 2 minutes until fragrant.
Pour in the chicken bone broth and tamari, bringing the liquid to a gentle simmer.
Add the baby bok choy to the broth and cook for 1-2 minutes until the leaves are wilted but the stems remain crisp.
Divide the cooked soba noodles into a bowl, pour the pork and broth mixture over the top, and finish with the halved egg and sliced green onions.