Shell shrimp and devein; reserve the shells. Sprinkle the shrimp with lemon juice; refrigerate.
Melt 4 tablespoons of the butter in a large frying pan over medium heat and add the shallots and carrot; cook until vegetables are soft and shallots are clear. Add the thyme, tarragon, sweet paprika, piment d’Espelette, and shrimp shells. Cook for five minutes over medium-low heat, stirring occasionally.
Increase the heat to medium-high, add tomato paste, mix well and cook for 30 seconds. Add the cognac and flambé. Lower the heat and add the white wine when the flames have subsided. Season with 1 teaspoon salt, and cook until the liquid has thickened a bit — about 3 minutes. Strain this shrimp base into a large stock pot and add the broth. Add the reserved shelled shrimp and bring to a boil. Lower the heat to a brisk simmer and cook for 10 minutes.
Pour the shrimp and broth into a blender, and blend until completely smooth. Strain back into the pot and discard solids. Reheat the soup for 2 to 3 minutes. Work together the remaining 2 tablespoons of butter and the flour (beurre manié), whisk it into the soup, and then add the cream. Continue cooking for 5 minutes. Season with salt and pepper to taste, and serve hot, sprinkled with parsley.