In a large pot, add 4 cups of water and the kombu seaweed (and shiitake mushrooms if using). Slowly bring the water to a simmer over medium heat. Just before it reaches a boil, remove the kombu and shiitake mushrooms to prevent a bitter taste. Discard the kombu but save the mushrooms for another use or chop them finely and return them to the pot if you prefer. Reduce the heat to low to keep the broth warm.
While the dashi is simmering, place the dried wakame seaweed in a bowl of cold water and let it soak for about 5 minutes until it becomes soft. Drain and set aside.
Add the cubed tofu to the warm dashi. Gently stir in the rehydrated seaweed.
In a small bowl, take a ladleful of warm dashi and mix it with the miso paste to create a smooth paste. Return the miso mixture to the pot.
Add soy sauce (if using) and sesame oil (if desired) to the soup. Stir gently to combine. Taste the soup and adjust the miso paste or soy sauce according to your preference for saltiness.
Ladle the miso soup into individual bowls and garnish with thinly sliced green onions.
