Remove the skin from the salmon and cut into largish chunks. Remove any small pin bones and discard. Reserve the skin.
Melt the butter in a soup pot and saute the leeks for 10 minutes, or until nice and soft.
While the leeks are cooking, put 5 cups of water and the reserved fish skin in a saucepan and bring to a boil, turn down the heat and simmer gently for 10 minutes. Note: if you are using fish stock you can skip this step.
Strain the broth and add to the pan with the leeks, along with the potatoes, carrots, and half of the fresh dill. Cook for another 10 minutes, or until the potatoes are just tender.
Add the salmon chunks to the soup along with the cream and allspice, and gently simmer on low heat until cooked through, just a few minutes. Add the remaining dill, and salt and pepper to taste.
If you can get your hands on great fish stock, by all means use it! Clam broth can also be used. I've sometimes even used clam juice as a base for fish soup.
I've occasionally made this soup with hot smoked salmon (the kind that comes in a chunk) and it gives great flavor.
Serve this soup with some rustic artisan style bread ~ rye or pumpernickel would be amazing! I have a great recipe for Pumpernickel Biscuits on the blog which would be perfect with this Finnish salmon soup
Consider doubling the recipe so you can have the leftovers the next day, it gets even better!