Bring salted water to a boil in a large pot. Add the shrimp and cook for 2 to 3 minutes, or until pink. Shell and devein them and reserve the shells. Simmer the shells with 2 cups water for 15 minutes.
Meanwhile, heat the oil in another large saucepan. Sauté the shallot until translucent. Add the leek and cook for about 3 minutes. Add the potatoes, carrot, and chicken broth.
Strain the shrimp stock, add it to the soup and stir. Reduce the heat and cook over medium heat for 20 minutes, or until the potatoes are tender. Puree the soup in a blender for just a few seconds so that some of the vegetables remain in chunks. If the soup is too thick, add more broth.
Add the shrimp and reheat the soup thoroughly. Season with salt, pepper, ginger, and tarragon. Stir in the cream and serve at once.