Fill an 8-quart kettle three fourths full with salted water and bring to a boil. Plunge lobster headfirst into boiling water and simmer, covered, 8 minutes. Immediately transfer lobster with tongs to a large bowl and cool.
When lobster is cool enough to handle, remove meat in the following manner, reserving shells and body: Break off claws at body of lobster. Crack claws and remove meat. Twist tail off lobster body and with kitchen shears cut thin hard membrane on underside of tail to remove meat. Chop tail and claw meat and chill, covered. Discard head sac from lobster body. With a sharp knife or kitchen shears chop or cut lobster body and reserved shells into pieces and chill, covered, for sauce.
In a 9-inch heavy skillet cook garlic and shallots in oil, stirring to not burn, just for 1 minute. Remove skillet from heat and add brandy. Carefully ignite brandy and cook over moderately high heat, shaking skillet, until flames die out. Add wine and water then add lobster shells. Stir well. Continue to cook mixture over simmer for 30 minutes.
Carefully remove from heat and pour lobster stock through a fine sieve into a large bowl. Press hard to release all the stock and juice from the bones, discard bones. . In a 3- to 4-quart heavy saucepan cook leek in oil over moderate heat, stirring, until softened. Add mushrooms, stir, cook for a few minutes, add more oil if needed. Add lobster stock, and reduce on simmer for 15 minutes. Add cream, stir well and reduce by half or until nicely thickened. Add lobster meat and incoporate gently. Season sauce with salt, pepper and cayenne.
Lay brioche on to sheet pans, heat oven to broil. Spray on top side of bread with pan spray, sprinkle with cheese. Place bread under broiler, and brown the cheese. Place two slices of bread on a plate, pour a generous amount of the lobster sauce/ mixture on top the bread. Garnish with chives.