Rinse the fish fillet, dry it and check for bones, removing them if necessary. Cut the skin with a sharp kitchen knife at intervals of one cm. Season the fillet on both sides with salt and pepper and dust the skin side with flour.
Cut off the stem end of the artichoke hearts, chop two-thirds of the bracts into small pieces, and chop the remaining bracts around the artichoke bottoms. Remove the “hay” with a teaspoon. Cut the artichoke bottoms into pieces just before using.
Preheat the oven to 200 °C.
In a roasting pan, sauté the shallots in a little olive oil, add the artichoke hearts, sauté and season with salt and pepper. Extinguish with white wine, add the clear soup and let it boil. Rinse tarragon, shake dry and spread evenly over the artichoke hearts.
Sauté the fish over medium heat in the remaining olive oil on the skin side.
Place the fish, skin side up, on the bed of artichokes and steam in the stove without the lid for about twelve minutes.
Remove the fish and keep warm in the oven. Remove the tarragon, season the artichoke hearts with salt and season with pepper. Portion the fish and serve with the artichoke hearts.