Heat 1 tablespoon neutral oil in a soup pot over medium heat. Add the shallot and sauté for 5 minutes until translucent.
Cook the mushrooms and sweet potato:
Add the shiitake mushrooms to the shallot and cook, stirring occasionally, for 5 minutes. Add the diced sweet potato and season with 1½ teaspoons kosher salt. Sauté over medium heat for an additional 3 to 4 minutes.
Simmer the broth:
Add 6 cups of water to the pot and bring to a boil. Reduce the heat to low. Add ¼ cup tamari, 2 tablespoons mirin, 1 tablespoon sesame oil, and 1 tablespoon chili oil. Add the cubed tofu and cover the pot. Simmer for 20 to 30 minutes or until the sweet potatoes are fork-tender.
Remove the lid from the pot and taste the broth. Add more tamari, mirin, sesame oil, or chili oil depending on your preference. If you feel the broth is too salty, you can add a few splashes of water to dilute it.
Cook the noodles:
Bring a large pot of water to a boil. Add the dry soba and cook for 4 to 5 minutes until tender. Drain and rinse. Divide the noodles between 4 bowls.
To serve:
Ladle the soup over the noodles. Garnish with sliced scallions. Enjoy!