Steam the lobster tails and when cool enough to handle, cut up the center of the underside membrane with a pair of shears, open like a butterfly and gently remove the meat.
Cut or chop into 1/3-inch chunks.
Set the shells aside to use in the sauce.
Cut enough brioche into 1/4-inch dice (like a crouton) to spread in a single layer covering the bottom of a shallow baking pan. Bake brioche in middle of oven until dry but not golden, about 12 minutes.
Next, finely chop white part of leek.
Then trim cremini stems flush with caps and discard shiitake stems. Cut cremini and shiitake caps into 1/4-inch dice.
In a 9-inch heavy skillet, cook leek in oil, covered, over moderately low heat, stirring occasionally, until tender, about 5 minutes.
Add mushrooms and sauté over moderately high heat, stirring, until tender and any liquid mushrooms give off is evaporated. Then remove skillet from heat and add brandy.
Carefully ignite brandy and cook over moderately high heat, shaking skillet, until flames die out.
Continue to cook mixture, stirring, until any remaining liquid is evaporated and season with salt and pepper. Transfer mixture to a bowl and stir in lobster meat.
In a large bowl whisk together yolks, egg, cream, cayenne, and salt to taste and gently stir in brioche croutons and lobster mixture.
Chill bread pudding, covered, until brioche is soaked with custard, 2 to 3 hours.
Bread pudding may be made up to this point 1 day ahead and chilled, covered.
Finely chop carrot, celery, and white part of leek separately.
In a 3 to 4-quart heavy saucepan cook leek in oil over moderate heat, stirring, until softened. Add carrot and celery then cook, stirring, until celery is slightly softened. Add lobster shells and sauté over moderately high heat, stirring occasionally, 2 minutes. Stir in tarragon.
Remove pan from heat and add brandy.
Carefully ignite brandy and boil mixture, shaking pan, until flames die out and brandy is evaporated. Add wine and water and simmer mixture, uncovered for 1 hour.
With a knife, halve vanilla bean lengthwise and scrape the seeds.
Pour lobster stock through a fine sieve into a large bowl, pressing hard on solids, and transfer liquid to cleaned pan.
Boil stock until reduced to about 1/2 cup. Stir in tomato purée and bring to a boil.
Then, stir in scraped Rodelle Vanilla Bean seeds, bean pod, and cream.
Simmer sauce until reduced to about 1 cup. Season sauce with salt and remove the vanilla bean pod.
Transfer to a small bowl and chill, covered, while baking puddings. Sauce may be made up to this point 1 day ahead and chilled, covered.
Preheat oven to 300°F. Spray 2 12-cup mini muffin tins with oil.
Divide bread pudding among muffin cups and arrange in a roasting pan.
Add enough hot water to roasting pan to reach one third up sides of tins and tent roasting pan with foil. Bake puddings in middle of oven 20 minutes.
Carefully remove foil and bake puddings until a knife inserted in centers comes out clean, 15 minutes more.
Remove tins from roasting pan and let puddings stand 5 minutes. Reheat sauce over moderate heat until hot and add chives.
Run a thin knife around edge of each pudding lift out. Arrange the puddings on a platter with the sauce in a bowl with small ladle in the center.
