Clean and wash the fennel, put the fennel greens aside. Halve the fennel and remove the stalk. Slice the fennel into thin slices. Peel onion and garlic, put 1 clove aside. Finely dice 2 cloves and onion.
Wash the salmon, dab dry and cut into cubes. Heat 2 tablespoons of oil in a saucepan, fry the salmon in it until golden brown, remove. Sauté onion, garlic and fennel in frying fat. Add tomato paste and sweat briefly.
Chop the tomatoes. Pour into the pot together with fish stock and 400 ml water, add bay leaf. Bring to the boil, stir in broth and simmer for 8-10 minutes at low heat. Add salmon cubes 2 minutes before the end of cooking time.
Dice the clove of garlic that has been put aside. Wash parsley, dab dry and remove leaves. Puree the garlic, parsley, fennel greens, parmesan and lemon zest with 75 ml olive oil in the universal chopper.
Season to taste with salt and pepper. Season soup with lemon juice, sugar, salt and pepper. Serve together with the pistou.