In a large saucepan melt 4 T of the butter over medium heat. Add the shallots and saute until softened, about 5 minutes.
Whisk in the flour and cook for 1-2 minutes. Slowly pour in the seafood stock and cream while whisking. Add in the lobster shells and cook over medium-low heat for 10 minutes. Remove the shells and discard.
Add in 2/3 of the lobster meat, tobasco and paprika; simmer for 5 minutes.
Working in batches, pour the soup into a blender and puree until smooth (conversely, you can use an immersion blender). Return the soup to the pot and add in the remaining lobster meat and 2 T butter. Simmer for another 5 minutes.
Ladle into bowls, sprinkle with fresh chives, and serve.