4 (1 ½ pound) lobsters
½ cup heavy cream
1 cup Lobster Stock
½ cup cognac
2 sticks (1/2 pound) plus 2 tablespoons unsalted butter, chilled
Salt and freshly ground pepper, to taste
1 (1-inch) piece ginger root, peeled
2 medium carrots, peeled
1 cup snow peas
1 pound fresh fettuccine
1 tablespoon extra-virgin olive oil
Bring a large stockpot filled with water to a boil. Plunge the lobsters headfirst into the water, submerging them completely, and boil for 9 minutes. Remove the lobsters from the boiling water and refresh in a bath of salted ice water. Break off the head cavity of each lobster, removing and reserving any coral or roe. Clean out the head, discarding the contents. Using kitchen shears, remove the lower part of the head shell, reserving the top of the shell with the antennae intact for garnish. Remove the tail and shell the claws, keeping the flesh whole, if possible. Using kitchen shears, cut off the bottom part of the tail shells and reserve for garnish.
In a large, heavy skillet, combine the cream, Lobster Stock, and cognac. Cook at a low boil over medium heat until reduced by half. Dice two sticks (1/2[frac] pound) of the chilled butter and whisk into the sauce, along with the reserved lobster coral. Strain the sauce through a fine sieve into a medium saucepan, season to taste with salt and pepper, and keep warm over very low heat. Cut the ginger, carrots, and snow peas into fine julienne, keeping each vegetable separate. Place the ginger in a small saucepan of cold water and bring to a boil. Drain and repeat this process two more times, using fresh, cold water.
Fill a large stockpot and a large saucepan with salted water and bring to a boil. Add the fettuccine to the stockpot and cook for 5 minutes, or until tender but still firm. Drain and toss with the olive oil. Add the carrots to the saucepan of boiling water and cook for 2 minutes. Add the snow peas and continue cooking for 1 minute more. Drain and toss the vegetables with the remaining 2 tablespoons of butter, seasoning to taste with salt and pepper. Combine the fettuccine and vegetables in a large bowl and toss very gently to mix. Arrange in nests on the center of four dinner plates.
Gently reheat the lobster meat in the lobster coral sauce. Arrange the tail and claw meat in the shape of a whole lobster on top of each pasta nest, using the head and tail shells for garnish. Spoon the remaining sauce over the plates and serve immediately.