How to Make It
In a large soup pot, heat the oil. Add the reserved shrimp shells and cook over moderately high heat until they turn pink, about 4 minutes. Add the carrots, celery and one-third of the onions; season with salt and pepper and cook until tender, about 5 minutes. Slowly add the brandy and cook until it has reduced to 2 tablespoons, about 4 minutes. Stir in the tomato paste and cook until the vegetables are well-coated, about 2 minutes. Add the peppercorns, tarragon sprigs, thyme, garlic, bay leaves and water and bring to a simmer. Cook until the shrimp broth is very flavorful and has reduced to 8 cups, about 45 minutes. Strain the shrimp broth into a large bowl and discard the solids.
Wipe out the soup pot. Add the butter and melt over moderate heat. Stir in the flour and cook, stirring, for 3 minutes. Add the remaining onions and the corn and cook until softened, about 5 minutes. Slowly whisk in the reserved broth. Bring to a simmer and cook over moderately low heat for 15 minutes. Raise the heat to moderate. Add the shrimp and cook until white throughout, about 3 minutes. Stir in the cream and season the soup with salt and pepper. Ladle the soup into bowls, sprinkle with the chopped tarragon and serve.