Step 1Heat 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 2Stir 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.