1 lemon half, plus 2 tablespoons fresh lemon juice
1 pound salsify
1 stick (4 ounces) unsalted butter
1/2 cup heavy cream
Pinch of sugar
6 tablespoons grapeseed oil
2 medium leeks, white and tender green, cut into 2-inch julienne
2 vanilla beans, split, seeds scraped
Fill the sink with ice water. Set a rack in a very large stockpot, add 5 inches of water and bring to a boil. Add 4 of the lobsters, cover and steam until bright red, about 11 minutes. Using tongs, transfer the lobsters to the ice water. Repeat with the remaining lobsters; add water to the pot if necessary.
Drain the lobsters and pat dry. Twist off the tails, claws and knuckles. Crack the shells and remove the meat. Slit the tails and pull out the intestinal veins. Using sturdy shears, cut the shells of 2 of the lobsters into 2-inch pieces; discard the remaining lobster shells.
In a large saucepan, heat the olive oil until shimmering. Add the shallot and cook over moderate heat until just beginning to brown. Add the garlic and cook until fragrant. Add the lobster shells and cook, stirring, until beginning to brown in spots, about 8 minutes. Add the wine and cook over moderately high heat until nearly evaporated, about 15 minutes. Add the demiglace and cook over moderate heat until slightly reduced, about 5 minutes. Strain the sauce into a medium saucepan, pressing hard on the shells to extract as much sauce as possible. Add the port, season with salt and pepper and simmer over moderately low heat for 5 minutes. Cover and keep warm.
Fill a bowl with water. Squeeze the lemon half into the water and add it to the bowl. Peel the salsify, cut it into 1-inch lengths and add it to the water.
In a large saucepan, combine 1 cup of water with the lemon juice, 6 tablespoons of the butter and a pinch of salt. Drain the salsify, then add it to the pan and bring to a boil. Cover and simmer over moderate heat until the salsify is tender and the liquid is reduced to a glaze, about 15 minutes. Add the cream and sugar and simmer for 1 minute.
Transfer the salsify mixture to a food processor and puree until very smooth. Season with salt and pepper. Return the puree to the saucepan and keep warm.
In a medium saucepan, heat 1/4 cup of the grapeseed oil until shimmering. Add the leeks and fry over moderate heat, stirring, until golden and crisp, 3 to 4 minutes. Using a slotted spoon, transfer the leeks to paper towels. Sprinkle lightly with salt.
In a small bowl, stir the vanilla seeds into the remaining 2 tablespoons of grapeseed oil.
In a very large skillet, melt the remaining 2 tablespoons of butter over moderately low heat. Add the lobster meat and cook until warmed through. Slice the tails crosswise into medallions. Mound the salsify puree in the center of 8 warmed dinner plates and arrange 2 claws and 1 tail around each mound. Spoon the Pinot Noir sauce around the lobster and top with the crispy leeks. Dot the plates with the vanilla oil and serve.
The salsify puree can be chilled overnight. The lobsters and sauce can be prepared through Step 8 early in the day. Chill the lobster. Reheat all of the components just before serving.
To save time, you can buy cracked, steamed lobsters for this dish.