Heat large pot over medium heat. When pot is warm, add 1 tablespoon olive oil. Swirl pot occasionally to distribute oil around pot.
When oil is hot and shimmery, add shrimp to pot. Cook shrimp 1 to 2 minutes, then flip shrimp over and cook another 1 to 2 minutes, until shrimp are pink on both sides.
Transfer shrimp to cutting board, then drain liquid from pot into bowl or glass jar. Set liquid aside. Chop shrimp into bite-sized chunks.
Return large pot to stovetop and increase heat under pot to high. When pot is warm again, add 2 tablespoons olive oil and swirl pot occasionally to distribute oil.
When oil is hot and shimmery, add shrimp shells to pot. Sauté shrimp shells, stirring occasionally, until shells begin to brown - approximately 4 minutes.
Once shells start to brown, add onion, celery, carrot, garlic, tomato, tarragon, thyme, bay leaves, and peppercorns to pot. Stir in brandy and sherry, until ingredients are well incorporated. Bring mixture to boil over high heat and allow to boil 4 minutes or until majority of liquid has evaporated.
Once brandy and sherry have mostly evaporated, reduce heat under pot to medium. Add 4 cups seafood stock and reserved shrimp cooking juices to pot, stirring well to incorporate liquids. Bring mixture boil over medium heat and boil 25 minutes or until liquid has reduced to 3 cups.
Use colander to strain liquid from pot into large bowl. Collect solid ingredients in colander and press firmly with back of spoon to expel as much liquid as possible. Discard solid ingredients.
Return liquid to large pot, and return pot to stovetop over medium heat. Add tomato paste and whisk until paste is incorporated into liquid. Simmer mixture 3 minutes.
While mixture simmers, add cornstarch and water to small bowl and whisk vigorously until cornstarch is dissolved and creates slurry.
After 3 minutes, remove pot from heat. Allow bisque to cool slightly, then pour in heavy whipping cream and cornstarch slurry. Stir until cream and slurry are well incorporated, then return pot to heat. Increase heat under pot to medium-high and simmer mixture 3 to 5 minutes or until slightly thickened.
When mixture has thickened, reduce heat under pot to medium. Add chopped shrimp and 2 tablespoons dry sherry, and stir to incorporate. Simmer mixture 1 to 2 minutes or until shrimp is warmed through. Be careful not to overcook shrimp.
Once shrimp is warm, ladle bisque into serving bowls. Garnish bowls of bisque with chopped chives and freshly cracked black pepper. Drizzle spoonfuls of heavy cream on top of bisque in circular motion, then serve bisque immediately with crusty bread if desired.