Bring a small pot of water to a boil, carefully lower the eggs into the water, and cook for 6 minutes and 30 seconds before transferring to an ice bath to peel and slice.
Cook the soba noodles in boiling water according to the package instructions, then drain and set aside.
In a large pot over medium-high heat, add the toasted sesame oil and ground pork, seasoning with sea salt and black pepper while browning until fully cooked.
Stir in the minced garlic, grated fresh ginger, and sliced shiitake mushrooms, sautéing for 3 minutes until the mushrooms are tender and fragrant.
Pour in the chicken broth, tamari, and sriracha, bringing the mixture to a gentle simmer to meld the flavors.
Add the baby bok choy to the pot and cook for 2 minutes until the leaves are wilted and the stems are just tender.
Divide the noodles into bowls, ladle the spicy broth and pork over them, and top with the jammy eggs and sliced green onions.