Bring a small pot of water to a boil and cook the egg for 6.5 minutes, then immediately transfer to an ice bath to stop the cooking.
In a separate large pot, cook the soba noodles according to package directions, drain, and set aside.
In the same large pot over medium-high heat, brown the ground pork with sea salt and black pepper until fully cooked and slightly caramelized.
Stir in the minced garlic and grated fresh ginger, sautéing for 1 minute until highly fragrant.
Pour in the beef broth and tamari, scraping the bottom of the pot to release any browned bits, and bring to a gentle simmer.
Add the chopped baby bok choy to the broth and cook for 2 minutes until the leaves are wilted and stems are just tender.
Stir in the toasted sesame oil and remove the pot from the heat.
Divide the cooked noodles into a deep bowl, pour the pork and broth mixture over them, and top with the peeled, halved egg and sliced green onions.