Set aside 2-2 sprigs of parsley and dill. Snip the rest of the herbs finely, and put them into a bowl together with the capers and add some grated lemon rind, too. Cut the pomegranate in half, and with the help of a spoon, release the seeds.
Cut the fish in half, salt it mildly and place it in a low pot with 150 g water, 3 slices of lemon, the shallots and the 2-2 sprigs of parsley and dill. Bring the liquid to a boil, and then cover the pot. Cook it slowly, at low heat, below boiling point, for about 12-14 minutes.
Prepare the gremolata: add the pomegranate seeds, together with the balsamic vinegar and the olive oil, to the finely chopped herbs. Mix it all thoroughly and sprinkle it with some sea salt. Finally, remove the fish from the pot and let it drip on a kitchen paper towel. Serve it fresh with the gremolata, the shallots and the remaining fresh lemon.