In a large pot, melt the butter over medium heat. Add the sliced leek and carrots, season with a pinch of salt and cook until softened, about 5 minutes.
Add the potatoes to the pot. Pour in the fish or vegetable broth, then add the bay leaf, pinch of allspice and season with salt and pepper. Bring the mixture to a boil, then reduce the heat to medium-low and let it simmer until the vegetables are tender, about 15-20 minutes.
Once the vegetables are cooked, gently stir in the salmon pieces. Let the soup simmer for an additional 5 minutes, or until the salmon is cooked through.
Pour in the cream and add lots of fresh dill, stirring well to combine. Do not let it boil.
Remove the bay leaf from the soup. Taste and adjust seasoning if necessary.
Pour the Finnish Salmon Soup into bowls and garnish with more freshly chopped dill and a squeeze of fresh lemon juice if using. Enjoy!
