Step 1 Heat a heavy-bottomed pot over medium-high heat until hot. Add the butter, and, when it is melted, stir in the leeks, mushrooms and garlic. Cook, stirring frequently, until the leeks are translucent and soft.
Step 2 Stir in the clam juice, crushed tomatoes, chopped parsley and dill, and season with the salt and pepper. Bring to a simmer, then stir in the salmon. Continue to simmer until the salmon is fully cooked, 3 to 5 minutes.
Step 3While the soup is cooking, whisk the flour into the heavy cream in a small bowl. Slowly add the cream to the soup when the salmon is cooked. Continue to simmer until thickened, about 5 minutes.
Step 4Ladle the soup into bowls, and serve garnished with dill sprigs.