Boil the soba noodles in a separate pot according to package directions, then drain and set aside.
Heat the toasted sesame oil in a medium pot over medium heat and sauté the minced ginger and garlic until fragrant.
Add the chopped kimchi and gochugaru to the pot, stirring for 2 minutes to develop a deep, smoky flavor.
Pour in the vegetable broth, tamari, and nutritional yeast, bringing the liquid to a gentle simmer.
Gently fold in the cubed extra firm tofu and shelled edamame, allowing them to heat through for about 5 minutes.
Add the chopped bok choy to the broth and cook for 1 minute until the leaves are just wilted and the stems are tender-crisp.
Place the cooked soba noodles into a large bowl, ladle the hot soup and tofu mixture over the top, and garnish with sliced green onions.