Bring a small pot of water to a boil, carefully lower the egg into the water, and boil for exactly 6 minutes and 30 seconds for a jammy yolk.
Immediately transfer the egg to an ice bath to stop the cooking, then peel and set aside.
Cook the soba noodles in a separate pot of boiling water according to package directions, then drain and rinse with cold water.
In a medium saucepan, heat the sesame oil over medium-high heat and add the ground pork, breaking it up with a spatula.
Season the pork with sea salt and black pepper, cooking until browned and cooked through.
Stir in the minced garlic and grated ginger, cooking for 1 minute until fragrant.
Pour in the beef broth and tamari, then add the sliced shiitake mushrooms and baby bok choy.
Simmer the broth for 3-5 minutes until the vegetables are tender but still vibrant.
Place the cooked soba noodles in a deep bowl and pour the hot broth, pork, and vegetables over them.
Slice the soft-boiled egg in half and place on top, garnishing with sliced green onions before serving.