1. To blanch the lobsters: Bring a large pot of water to a boil. Prepare an ice bath; set aside. Remove the tails and claws from lobsters. Place lobster tails into the boiling water, and cook for 3 minutes. Transfer to ice bath to stop cooking. Place the lobster claws in boiling water, and cook for 6 minutes. Transfer to ice bath to stop cooking. Remove meat from tails and claws; cut tail meat in half lengthwise; set aside.

2. Remove the bodies from the shells and rinse; discard shells. Cut bodies into chunks; set aside.

3. To make the broth: Heat oil in a large stockpot over medium heat. Add the onion, carrot, fennel, celery, and garlic. Cook, stirring occasionally, until onions are translucent, but not brown, about 5 minutes. Add the lobster body chunks. Raise heat to high, and cook until lobsters are translucent and sweaty about 2 minutes. Add wine, and bring to a boil. Cook until reduced by three-quarters, about 5 minutes. Stir in the thyme, tarragon, and carrot juice. Bring to a boil. Reduce to a simmer and cook for 30 minutes.

4. Whisk the egg whites into carrot broth. Return to a simmer and cook until egg whites have coagulated (the egg whites will help remove the impurities resulting in a clear broth). Strain through a cheesecloth lined sieve into a clean saucepan and keep hot.

5. To prepare the vegetables: Preheat oven to 300 degrees. Remove the outer leaves of the artichokes by snapping them off at the base. Slice off the green tops, then cut off the stems at the base. Use a melon baller to remove the chokes. Place artichokes in a small baking pan and cover with oil. Bake until tender when pierced with the tip of a knife, 35 to 45 minutes. Remove from oven and let stand until cool enough to handle. Remove from oil and cut into 1/2-inch wedges; set aside in a medium bowl. Reserve oil.

6. Bring a large pot of salted water to a boil. Add the peas to the boiling water and cook until bright green, about 2 minutes. Use a slotted spoon to transfer to the bowl with the artichokes; set aside. Add asparagus to boiling water and cook until bright green, about 2 minutes. Use a slotted spoon to remove from boiling water and add to the artichokes and peas. Drizzle vegetables with about 1 teaspoon of the reserved oil; reserve the remaining oil for another use. Season vegetables with salt, pepper, tarragon, and parsley.

7. To assemble the dish: Heat beurre blanc in a medium saucepan over medium-low heat. Add lobster meat, and heat through. Be sure not to let it boil, or it will separate. Use a slotted spoon to remove lobster from beurre blanc, and drain on a paper towels. Blot off excess beurre blanc with a clean kitchen towel.

8. Divide vegetables between 6 warm bowls. Place one tail and two claws in each bowl. Serve with broth ladled over lobster just before serving. Serve immediately.