Put water and kombu in a pot and let it sit for at least 30 minutes until the kombu softens.
Heat the pot over very low heat for about 10 minutes or longer. When small bubbles start to appear on the surface, remove the kombu. Kombu dashi is ready.
Sprinkle sake over the salmon fillet and let it sit for about 5 minutes to reduce any fishy odor.
Remove any scales from the fillet, then cut it into bite-sized pieces. Cut the potato, carrot, Japanese leek, and cabbage into bite-sized pieces as well.
Bring the kombu dashi in the pot to a boil, then add the salmon, carrot, and potato. Reduce the heat to low and simmer for about 10 minutes until tender, skimming off any scum.
Add the leek, cabbage, and sake to the pot and continue simmering for a few more minutes. Turn off the heat, then dissolve the miso using a ladle and chopsticks.
Serve in bowls and top with butter to taste.