Clean the head of the salmon and put to boil in cold water for about 15 minutes. Remove the head and cool it down. Meanwhile, dice the vegetables and strain the fish broth.
Return it to the heat and add to it the cleaned meat from the head and pieces of salmon with all the vegetables. Simmer over low heat for 15 minutes, then add the spices.
Remove the fish soup from the heat and add the chopped fresh parsley. Serve each serving of soup with a slice of lemon and a sprig of parsley.