Have the sole fillets raised by your fishmonger. Cut each fillet in half. Cook the lobsters in court-bouillon, shell them and slice the flesh.
Present the red peppers over a flame or place them in a very hot oven until the skin burns. Then rub them between your hands under running water, the skin will come off on its own. Open the peppers in half, remove the stems and cut the peppers into nice strips of about 2 centimeters.
Put the olive oil in a sauté pan and, when very hot, sear the pieces of sole and the lobster rolls previously salted and peppered. Brown well on each side and add the pepper strips. Sear them too in the oil. This should take about 6 minutes.
Degrease and add the vodka, reduce until only a teaspoon of liquid remains. Then wet with the American sauce, remove the various ingredients and reserve them in a sheet of absorbent paper.
Let the cooking reduce and pass it through a fine sieve. Return to the heat, adding the cream.
Arrange the soles, lobster and peppers harmoniously on 4 plates. Go warm.
Finish the sauce by incorporating the lobster butter in pieces and making a rotating movement with the sauté pan. Season with salt and pepper.
Coat the ingredients with sauce and garnish with sprigs of chervil or julienned radish.
My advice:if you don't have lobster butter, use fresh butter. You can also make your American sauce with the lobster carcasses.
Joëlle's point of view:When wild mushrooms are in season, I advise you to add some fresh chanterelle mushrooms to this recipe that you have blanched and sautéed in butter.