Sprinkle salt on the buri fish head, place it in a bowl, cover with plastic wrap, and refrigerate for 30 minutes. Pour boiling water over the fish, rinse off slime and blood under running water, and pat dry with paper towels.

Cut daikon and carrot into quarters lengthwise, then slice thinly. Slice the green onion into small pieces.

In a pot, add the buri fish head, sake, and water. Heat over medium heat and skim off any foam. Simmer for 15 minutes, then add daikon and carrot and cook until tender.

Turn off the heat and dissolve miso paste into the soup. Warm gently without boiling.