Lobster Eggs Benedict

Preheat a broiler.

Remove the claws, knuckles and tail from each lobster body; reserve bodies for another use. Remove the meat from the claws, knuckles and tails; reserve the shells. Cut the tail meat crosswise into 1/2-inch-thick slices; refrigerate along with the claw and knuckle meat until ready to use.

In a sauté pan over medium heat, melt the 4 Tbs. butter. Add the shallots and cook, stirring occasionally, until translucent, about 3 minutes. Add the reserved lobster shells and cook, stirring occasionally, until the shallots are golden and any liquid has evaporated, about 5 minutes. Off the heat, add the cognac, then return the pan to medium heat and cook until the liquid has almost evaporated, about 3 minutes. Add the cream and cook until reduced by half and thickened, 7 to 10 minutes. Strain the sauce through a fine-mesh sieve into a double boiler set over very low heat. Add the tarragon, lemon zest, salt and pepper.

Lightly spread the cut sides of each brioche or muffin half with 1 tsp. of the butter and broil until golden, 3 to 5 minutes. Turn off the broiler, cover the brioche or muffin halves with aluminum foil and keep warm in the oven.

Fill an egg-poaching pan with 1/2 inch water, set over medium heat and bring to a simmer. Lightly coat the poaching cups with nonstick cooking spray and crack an egg into each cup. Cover and cook until the whites are firm and the yolks are glazed over but still soft, about 3 minutes, or until done to your liking. Transfer the eggs to a warmed plate; repeat with the remaining eggs.

Add the reserved lobster meat to the sauce and heat until warmed through, about 3 minutes. Place 2 brioche or muffin halves on each of 4 warmed plates. Using a slotted spoon, transfer the lobster meat to the brioche or muffin halves, dividing evenly. Top each with an egg and some of the sauce. Sprinkle with the chives. Serve immediately.