Turn pot on medium-high heat. Right before the water starts to boil (bubbles start to break around the edge of the pot), remove kombu and scatter the katsuobushi over the surface of the water. Reserve kombu to make niban dashi (second broth) or compost.
Let broth return to boil, then turn off heat and let sit 5 minutes.
The flakes will have sunk to the bottom of the pot. Strain the stock through a tight mesh strainer. You now have dashi.
Ladle 1 cup dashi into a small bowl. Let cool slightly, then add miso paste and whisk until smooth.
Add the miso mixture back to the dashi and whisk to combine. Return to a slight simmer, being careful not to boil the mixture.
Add scallions and mushrooms and cook for another minute.
Remove from heat, ladle into soup bowls and serve immediately.