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 to cool.
Cook the soba noodles in boiling water according to package directions, then drain and rinse with cold water to prevent sticking.
Press the tofu with a heavy object for 10 minutes to remove excess moisture, then cut into 2cm cubes.
Heat half of the sesame oil in a pan over medium-high heat and sear the tofu cubes until golden brown on all sides, seasoning with a pinch of salt.
In a medium pot, heat the remaining sesame oil and sauté the minced garlic, grated ginger, and sliced shiitake mushrooms for 3 minutes.
Pour in the vegetable broth and tamari, bringing the liquid to a gentle simmer for 5 minutes.
Add the baby bok choy and edamame to the broth and cook for 2 minutes until the greens are tender and bright.
Divide the noodles into a large bowl, pour the hot broth and vegetables over them, and top with the seared tofu and the peeled, halved jammy egg.