Wash the salmon heads well to remove any blood or gills. Gills will ruin the broth by making it bitter and cloudy. Cover the heads with water in a large pot or Dutch oven. Add the onion, kombu and ginger and bring to a bare simmer. Do not let this boil. Simmer gently for 20 to 30 minutes.
Strain the broth and save the heads. Pick out all the meat from the heads, especially the cheek meat. Reserve in a bowl.
Return the broth to a clean pot and add the mirin. Heat but do not let boil. Add the soy sauce. If the broth still needs salt, add salt -- not more soy sauce, as that will make the broth too dark.
Bring another pot of salted water to a boil: This is for the noodles. Cook the noodles according to the directions on the package.
Ladle out some broth into soup bowls. Add a heaping teaspoon of miso (or more) to each bowl and stir to combine. Portion out the noodles to each bowl. Add the salmon meat on top of the noodles. Each person should get at least one cheek. Cover with more broth, garnish with chives and sliced chiles and serve at once.