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Prepare and chill the pie dough as directed in the recipe.
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2
To cook the lobsters: place the lobsters in the freezer for 20 to 30 minutes to numb them.
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Fill a large srockpot three-quarters full with cold water and add the sea salt.
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Bring to a rapid boil over medium-high heat.
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Transfer the immobile lobsters to a cutting board.
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Working with 1 lobster at a time, and holding the lobster securely with a kitchen towel to protect your hands, insert the tip of a chefs knife at the base of the head, parallel to the body, and swiftly cut completely through the head between the antennas.
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Use a sideways twist to break the claws, knuckles, and tails off of the lobsters.
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Reserve the bodies for making the sauce.
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Place the claws and knuckles in the boiling water and boil for 1 minute.
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Add the lobster tails and continue to boil for an additional 4 minutes (the tails will be only cooked about halfway).
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Using a slotted spoon, transfer all the lobster pieces to the ice bath; let sit for at least 5 minutes to ensure the cooking process has stopped.
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To remove the meat from the claws, pull the thumb of the claws off and remove the inner cartilage.
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Lay the claws flat on a cutting board and carefully tap with the blade of a chefs knife to crack.
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Gently wiggle the meat out from the shell and place it in a large bowl.
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Using kitchen shears, cut open the knuckles and discard the shells.
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Add the lobster meat to the bowl.
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Lay the lobster tails on a cutting board, shell side up, and hold with a kitchen towel to steady.
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Using a serrated knife, make 3 cuts crosswise between the joints so that you have 4 sections, including the tail fan.
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Add the lobster pieces to the bowl.
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Cover the bowl with plastic wrap and transfer to the refrigerator to chill until ready to use.
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The lobster may be prepared a day in advance.
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When cleaning the lobster bodies, it is best to wear kitchen gloves to protect your hands.
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Firmly pull the bodies and shells apart.
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When all of the bodies have been separated, use a tablespoon to scrape off the feathery gills and clean out the roe and innards from the underside of the shell.
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Coarsely chop the lobster shells and bodies.
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To make the sauce: Place a large stockpot over medium-high heat and coat with 2 tablespoons of the oil.
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When the oil gets hazy, add the cleaned lobster shells and bodies.
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Cook, stirring often, until the shells are well seared and bright red, about 3 to 5 minutes.
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Shells equal flavor.
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To keep the alcohol from flaming, remove the pot from the heat and pour in the brandy.
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Carefully return the pot to the stove and cook until the brandy is almost totally evaporated.
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Push the shells to the sides of the pot and add the remaining 2 tablespoons of oil and the celery, garlic, onion, carrot, and fennel.
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Cook, stirring occasionally, until the vegetables are tender and begin to caramelize, 10 to 15 minutes.
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Stir in the tomato paste and cook for about 2 minutes until the color deepens.
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Add the wine and stir to deglaze the pot, scraping up the bits from the bottom with a wooden spoon.
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Continue cooking until all of the liquid is evaporated, about 1 minute.
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Add the cream, thyme, bay leaf, peppercorns, and coriander.
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Reduce the heat to low and simmer until the sauce turns light orange and tastes like lobster, 15 to 20 minutes.
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Pass the sauce through a fine-mesh strainer into a clean saucepan to remove the solids, using a spoon or spatula to press out all the juice.
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Place over medium heat and bring the lobster cream to a simmer.
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Season lightly with salt and pepper.
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Remove from the heat and set aside.
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In a small saucepan, slowly melt 1 tablespoon of the butter over low heat.
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Just as the foam subsides, sprinkle in the flour, stirring constantly with a wooden spoon to cook the starchy taste out of the flour.
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Cook for 1 minute, without allowing the flour to color.
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Slowly whisk the roux into the lobster cream.
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Cook for 1 minute, stirring constantly to prevent lumps.
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The lobster cream should be thick enough to coat the back of a spoon.
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Remove from the heat.
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Cover to keep warm.
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To prepare the filling: Place a saute pan over medium-high heat.
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Add the butter and once it gets foamy, add the mushrooms.
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Season with salt and pepper and saute until the mushrooms release their moisture and begin to brown, about 3 to 4 minutes.
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Remove from the heat.
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Place an equal portion of the sauteed mushrooms, onions, carrots, potatoes, zucchini, and yellow squash evenly into each souffle dish.
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Remove the lobster meat from the refrigerator and place the equivalent of 1 whole lobster into each dish.
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Ladle 1/2 cup of the warm lobster cream sauce into each dish, sprinkle with the chopped herbs, a drizzle of truffle oil, and a few slices of black truffle.
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Preheat the oven to 425F.
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To assemble: remove the dough from the refrigerator and set it on the counter for 5 minutes to warm up and to make it easier to roll out.
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Sprinkle the counter and a rolling pin lightly with flour.
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Roll the dough out to a 1/4-inch thickness.
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Cut the dough into 4 circles, 1 inch larger than the diameter of the souffle dishes (you need four 1-quart dishes).
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Using a pastry brush, lightly coat the outer edges of the pastry circles with the egg wash.
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Carefully cap each dish with a pastry circle, egg wash side down, pressing the dough around the rim to form a tight seal.
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Brush the tops very lightly with egg wash and sprinkle with a little salt (preferably sea salt).
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Set the dishes on a baking sheet and transfer to the oven.
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Bake for 30 minutes, rotating halfway through cooking, until the potpie is puffed and golden.
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To serve: run a knife around the inside rims of the souffle dishes.
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Using a fork and spoon, carefully remove the dome cap and place it in the center of a serving plate.
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For a great presentation, arrange the pieces of lobster on top of the pastry, scatter the vegetables decoratively all around, and drizzle the lobster cream sauce over everything.
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Place the flour and salt in the food processor and pulse to combine.
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Add the butter cubes, a few at a time, pulsing until the mixture looks like small peas.
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Slowly add the ice water, a little at a time, until the dough starts to come together without being too wet or sticky (you may not need all the water).
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Pinch a small amount together; if it is crumbly, add more ice water, 1 teaspoon at a time.
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Form the dough into a disk and wrap in plastic wrap.
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Transfer to the refrigerator and chill for at least 1 hour.
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The dough can be made 1 day in advance.
