For the lobsters, kill them with a knife. Poach and shell the claws and clean the shells. Cut the flaps of shell off the ends of the raw lobster tails. Turn the tails upside down and use a large knife to split them in half lengthwise. Pull out the intestine. Cover the lobster claws and tails and refrigerate.
Heat 3 tablespoons of oil in a 10-inch pot over high heat until just smoking. Add the lobster shells, cover the pot, and sear, stirring often to prevent burning, until the shells turn dark red, about 3 minutes. Add the garlic, shallots, fennel, and tomato paste. Turn the heat to low, and cook, covered, until the vegetables begin to soften, about 8 minutes.
Raise the heat to high, add the brandy, and ignite it with a match to bum off the alcohol (the flame will go out by itself). Cook for 30 seconds. Stir in the lobster stock, shrimp stock, or water. Add the tarragon and ¼ teaspoon of pepper. Bring to a boil. Lower the heat slightly and simmer rapidly for 12 minutes, pressing down on the shells with a wooden spoon from time to time. Remove from the heat and let stand for 10 minutes.
Strain, pressing firmly on the solids to extract as much of the flavorful liquid as possible.
Put the strained liquid in a saucepan and simmer, spooning off the fat as it rises, until reduced to 1 cup, about 15 minutes. Whisk in the cream and butter. Season with salt to taste. Cool and refrigerate if making ahead.
For the mushrooms, heat the com oil in one of the skillets over high heat. Add the cepes, garlic, thyme, salt, and pepper. Saute until browned and softened, about 5 minutes. Discard the garlic and thyme. Set aside.
For the risotto, put the butter, garlic, and onion in an 8-inch saucepan over low heat. Cook until the onion is very soft, about 7 minutes. Meanwhile, bring the chicken stock to a boil in a medium saucepan. Adjust the heat so the stock simmers.
Stir the cepes into the onion. Stir in the white wine and bring to a boil. Stir in the rice. Stir ¼ cup of chicken stock into the rice mixture. Stir constantly and gently with a wooden spoon, adjusting the heat so the mixture simmers at all times, but does not boil.
When the mixture becomes very thick but not dry, stir in another ¼ cup of stock. Continue stirring and adding stock as needed for 10 minutes. Stir in the asparagus tips and continue the same process as before, until the rice is almost tender, about 10 minutes more. Stir in the heavy cream. (The recipe can be made to this point early on the day you plan to serve; cool and refrigerate the risotto.) If serving immediately, stir until the rice is tender, 2 to 3 minutes more. Keep warm.
. To serve, reheat the risotto, if necessary, and the sauce. Season the lobster meat with salt and pepper. Put 1 tablespoon of oil in each skillet and place over high heat. When just smoking, divide the lobster tail meat between the skillets, cut side down. Put half of the thyme around the edge of each skillet. Cook until the lobster is browned on the bottom, about 2 minutes. Turn the tails over, add 1 teaspoon of oil to each skillet, and lower the heat to medium. Cook until the meat turns opaque, about 2 minutes more. Remove from the skillets and keep warm.
. Place the large pieces of claw meat in the skillets and cook just until a metal skewer inserted in the center for 5 seconds feels hot when touched to your lip. Add the small pieces of claw meat and heat for a few seconds. Leaving the shell on, use a small knife to loosen the tail meat from the shell for easier eating.
. Stir the cheese, salt, pepper, and truffle oil, if using it, into the risotto. Spoon the risotto onto the center of 4 dinner plates, making sure the asparagus is evenly distributed. Over each risotto, arrange 2 half-lobster tails perpendicular to each other, 1 shell side down and 1 shell side up. Distribute the claw meat around the tails. Pour the sauce around the risotto and serve immediately.
