Fill a stock pot 3/4 full with cold water. Set over high heat, and bring to a rolling boil. Prepare an ice bath. Add the lobsters to the pot, making sure that each lobster is completely submerged in water. Cook lobsters about 8 minutes. Using tongs, transfer lobsters to an ice bath to cool. Drain lobsters in a colander.
Carefully remove lobster meat from the tails, claws and legs, being careful not to remove any cartilage from the claw meat. Cut the meat into bite-size pieces. Transfer meat to a bowl, cover with plastic and refrigerate until ready to use. Discard lobster bodies, but reserve the shells from the tails, claws and legs for making stock.
Melt 2 tablespoons butter in a large saucepan set over medium heat. Add chopped onion and celery to pan. Coarsely chop 1 leek and 2 carrots; add to pan. Add reserved lobster shells, 4 sprigs tarragon, and enough water to cover shells by 3-inches.
Bring liquid to a boil, reduce heat, and simmer, skimming surface often, until the stock is flavorful, about 1 1/2 hours.
Prepare an ice bath. Strain stock through a fine sieve, pushing down on solids to extract liquid. Transfer stock to a clean saucepan, and discard solids. Continue cooking stock until liquid has reduced to 2 cups. Remove from heat, and transfer to ice bath to chill. Transfer chilled stock to an airtight container; refrigerate until ready to use.
Split the remaining leek lengthwise. Cut the leek and remaininng 2 carrots into 1/2 -inch pieces; setaside.
Melt the remaining 2 tablespoons butter in a medium saucepan set over medium-low heat; sprinkle flour into saucepan, and cook, stirring constantly, so mixture foams and forms a paste, but does not brown, about 2 minutes.
Carefully add sherry, stirring constantly, to loosen any flour that has cooked onto the bottom of saucepan, being careful that no lumps form. Add tomato paste and 2 cups reserved lobster stock. Add the chopped leek and carrot to the saucepan. and cook untl just tender, about 4 mintues. Stir in cream and bring to a boil. Reduce heat, and simmer until sauce just starts to thicken, 5-6 minutes. Add salt and pepper . Pick tarragon from remaining 4 sprigs, chop, and add.
In a small bowl, ehisk egg yolk. Add a ladleful of hot sauce to temper the yolk; whisk to combine. Return mixture to saucepan over low heat; whisk to combine. Remove from heat.
Preheat oven to 350°F Set six 6-oz ramekins into a large roasting pan.
Add the reserved lobster meat to the sauce; stir to combine. Divide the Newburg evenly among the ramekins. Transfer the roasting pan to oven, and pour 1-inch boiling water into roasting pan. Cook until Newburg bubbles, about 25 minutes. Remove roasting pan from the oven, and carefully transfer ramekins to serving plates. Serve the Newburg immediately.