Preheat oven to 450 degrees F.
To make veloute: Melt the butter in a saucepan, and add the flour. Stir the mixture and cook for 2 minutes. Add the fish stock to the roux, and whisk in the cream. Bring the veloute to a boil and season.
Prepare Lobsters: To prepare the lobsters, use a sharp knife, and cut the lobsters lengthwise. Place the lobster flesh down in a hot pan. Do not add the butter until halfway cooked.
Once the lobster is halfway cooked, remove from pan. Remove the flesh from the tails, and chop meat. Mix the brunoise vegetables, lobster, and the fish veloute. Refill the lobster shells with the mixture, cover with the remaining sauce, and sprinkle with Gruyere. Bake in oven until nice and brown, approximately 5 minutes.
To assemble: Place lobster in the center of the plate. Decorate with cooked vegetable, and sprinkle Gruyere around the plate.
This recipe was provided by a chef, restaurant or culinary professional. It has not been tested for home use.