Remove the skin from the light side of the fish. Cut out the gills, drizzle the fish with lemon juice. Cut the shrimp lengthways in the middle so that the halves are still connected at the end of the tail, and remove the intestines from the shrimp.
Finely chop the shallots, sauté in butter in a small saucepan and deglaze with the prosecco. Reduce the liquid by half. Add creme fraiche and tarragon mustard and reduce to half again. Remove from heat, pass through a hair sieve and press the shallots through as much as possible. Season to taste with salt and cayenne pepper and set aside the sauce base.
Grease a baking sheet with olive oil and the same amount of butter and place the fish on it with the dark side down; only the fish, shrimp are added later. Make about 60-80 g butter liquid, add the pressed garlic and the finely chopped parsley and brush the fish and shrimp with the mixture. Preheat the grill in the oven.
Bring the water to a boil and prepare the linguine. Put the baking sheet with the fish in the oven, distance to the grill approx. 10-12 cm, cooking time approx. 15-20 minutes, depending on the size of the fish.
Drain the finished linguine, put it back in the saucepan and fold in at least 50 g butter. Place the prawns on the baking sheet 4 minutes before the fish is cooking. Bring the sauce base to the boil again, take it off the stove, add the egg yolks and assemble with the hand blender, keep the sauce warm and stop boiling.
To serve, place the linguine in the middle of the preheated plates. Fillet the fish and place on top of the pasta with the prawns. Mix up the sauce again and put it in a circle around the pasta.
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