Peel the shrimp, reserving the shells.
In a large stock pot, over medium high, heat the oil. Add the shrimp shells. Season with salt and pepper. Saute for 4 minutes. Add the mirepoix. Season with salt and pepper. Saute for 4 to 6 minutes, or until tender. Carefully add the brandy and flame, shaking the pan back and forth a couple of times. After the brandy has cooked off, stir in the tomato paste. Cook for 2 minutes. Add the garlic, bay leaves, tarragon, thyme, and peppercorns. Stir in the water. Bring the liquid to a boil. Reduce the heat to medium and simmer for 45 minutes.
In a mixing bowl, combine the flour and butter, mix well to form a beurre manie from the mixture into a long about 1-inch thick. Wrap the mixture in plastic wrap and chill until firm.
Strain the liquid. Wash out the stock pot and place the liquid back into the pan and bring the liquid back to a simmer. Whisk in the beurre manie a small piece at a time. Cook for 20 minutes. Whisk in the cream. Season with salt and pepper. Remove from the heat and cool completely. Refrigerate until completely chilled, about 2 hours.
Preheat the smoker. Season the shrimp with salt and white pepper. Place the shrimp in the smoker and smoke for 6 to 8 minutes, or until the shrimp turn pink and the tails curl in. Remove from the smoker and cool. Remove the soup with the refrigerator and season with salt and pepper. To serve, ladle the soup into each bowl. Garnish each soup with 2 shrimp, tarragon and a splash of brandy.
Recipe courtesy of Emeril Lagasse, copyright 1998