Press the tofu between paper towels to remove excess moisture, then cut into bite-sized cubes.
Bring a small pot of water to a boil and cook the soba noodles until tender; drain and rinse with cold water to prevent sticking.
In the same pot, soft-boil the egg for 6.5 minutes, then immediately transfer to an ice bath before peeling and halving.
Heat the toasted sesame oil in a large saucepan over medium-high heat and sear the tofu cubes until the edges are golden and crisp.
Add the minced garlic, ginger, and shiitake mushrooms to the pan, sautéing for 3 minutes until the mushrooms have softened.
Pour in the vegetable broth and tamari, then whisk in the miso paste until completely smooth and bring to a gentle simmer.
Stir in the chopped bok choy and edamame, cooking for 2 minutes until the greens are tender and bright.
Place the cooked noodles into a deep bowl, ladle the hot broth and tofu mixture over them, and top with the halved egg, green onions, and red pepper flakes.