Remove lobster head and claws. Using a large knife cut the tail shells between natural joints into 1-inch thick slices. Remove flippers from the last slice. Reserve one piece of lobster meat (finely shredded) to add to the artichoke mushroom salad. Place some clarified butter into heated pan and add lobster medallions. Saute for 1 minute and turn. Add the 1/2 finely diced onion, salt and dry white wine. Cover the pan, reduce heat and cook for 2 more minutes. Add tarragon. Strain the juices from the pan and discard the onion. Place the lobster back into the pan. Add 2 ounces fresh butter and 2 tablespoons of the sherry and stir until combined. Cover and poach for 5 minutes.
Meanwhile, for the salad, place alot of clarified butter into another very hot pan. Into the pan with the butter add the 1/2 finely sliced onion, garlic and the reserved piece of lobster. Add freshly ground pepper to the pan with the lobster, garlic and onion. Add pimento.
Into a bowl place the artichoke bottoms, the olive oil and the wine vinegar. To the bowl add the mushrooms and the lemon juice. Place the lobster medallions onto a heated serving dish with round part of the shell facing the outside. Strain the sauce onto the lobster. To the bowl, add the contents of the other pan with the mushrooms. Add a dash of sherry to the bowl and toss.