Add the mushrooms juice in the kettle and boil until the sauce has reduced to 2 cups. Bring to the simmer.
Cook the flour and the butter slowly in another saucepan for 2 minutes. Add to the sauce, stir it well. Boil during 1 minute while stirring. When done, add cream to the top.
Split the lobsters in two lengthwise. Remove the black thing around the eyes and the intestine. Take the coral and the liver, crushed them in a mixing bowl, and blend the mustard, half cup of whipping cream, egg yolks. Add the sauce while beating.
Heat the sauce again, bring it to the boil while stirring. Then boil slowly for 2 minutes. Add whipping cream with a tablespoon Taste and correct seasoning. Add a spoonful of cream on the top. Set aside.
Take the meat from the lobster and cut it into cubes. Put butter in a skillet over moderate heat. After 1 minute, stir in the lobstermeat, stir slowly, for 5 minutes. Pour in the cognac and boil until the liquid has reduced by half. Shake the skillet from time to time.
Add the mushrooms and two-thirds of the sauce in the skillet.
Arrange in a roasting pan the meat, sauce and mushroom in the shells. Sprinkle with cheese. Put the roasting pan in the oven at 220°C for 15 minutes until sauce is browned.