Heat the broth: Transfer the vegetable broth to a medium saucepan. Bring the liquid to a simmer over medium heat. Reduce the heat to low.
Optional: Transfer the tofu and an additional 2 cups mushrooms to a large baking sheet. Toss with a drizzle of olive or sesame oil, a dash of garlic powder, and salt to taste. Bake at 400ºF for about 15 minutes, or until the mushrooms are golden brown, tossing them after 10 minutes.
Add the veggies: Add the cabbage, one-half of the chopped green onion, and (the remaining) 2 cups mushrooms to the simmering vegetable broth and simmer for 5 minutes.
Dissolve the miso: Meanwhile either mix the miso, water, and sesame seeds in a small bowl or blend in a small chopper until smooth. Set aside.
Add the tofu and seaweed and simmer for about 2 minutes more, or until the tofu is warmed through.
Remove the saucepan from the heat and mix in the dissolved miso.
For serving: Serve over cooked noodles. Garnish with the remaining chopped green onion, and the baked mushrooms and chili oil, if using.
