Fill a large stockpot 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 for 8 minutes.
Using tongs, transfer lobsters to ice bath to cool. Drain lobsters in a colander.
Carefully remove lobster meat from the tails, claws, and legs, being careful to remove any cartilage from the claw meat. Cut the meat into bit-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 1.5 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 remaining 2 carrots into 0.5 - 1 inch pieces; set aside.
Melt the remaining 2 tbsps 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 turn 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 until just tender, about 4 minutes.
Stir in cream, and bring to a boil. Reduce heat and simmer until sauce just starts to thicken, 5 to 6 minutes. Add salt and pepper. Pick tarragon from remaining sprigs, chop, and add.
In a small bowl, whisk 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.
Add the reserved lobster meat to the sauce, stir to combine, and cook until Newburg bubbles, about 25 minutes