Fill a large bowl with ice water. Bring 6 cups water, tarragon, thyme, and salt to a boil in a 6- to 8-quart pot over medium-high heat. Add lobster tails. Return to a boil; reduce heat to medium. Simmer until shells turn bright red and meat is tender, 6 to 10 minutes. Remove tails and immediately plunge into the ice water.

When cool enough to handle, remove meat from shells. Return shells to pot. Simmer, covered, over medium heat to develop flavor, about 30 minutes.

Coarsely chop lobster meat and chill, covered, until ready to use.

Strain 4 cups of stock through a fine-mesh sieve into a large glass measuring cup; discard solids.

Melt butter in the same pot over medium heat. Cook chopped celery, stirring until tender, about 10 minutes. Stir in garlic; cook until fragrant, about 1 minute.

Stir in flour to coat vegetables. Add wine and tomato paste. Cook, stirring frequently, until mixture is combined. Stir in stock; cook over medium-high heat until mixture is bubbly. Cook mixture, stirring frequently, 2 minutes more.