Melt 1/4 cup butter in a large soup pot over medium heat. Add the onion, carrot, celery, and plum tomato. Cook, covered, for about 12 minutes, stirring every once in a while. The vegetables should be soft.
Raise the heat to high and add the shrimp shells and rice. Continue to cook, stirring, until the mixture is a deep red color, about two minutes. Add the tomato paste and continue to cook, stirring, until the mixture is caramelized, about two minutes more.
Now remove the pot from the heat and pour in 1/2 cup of sherry. Return to a high heat and cook until almost dry, about 1 1/2 minutes. Tie the parsley, thyme, and bay leaf together with kitchen string and add to the pot. Pour in the water and salt, then bring to a boil. Lower the heat and simmer the mixture, covered, for about 30 minutes.
Remove from the heat and cool. Remove and discard the tied bundle of herbs.
Working in small batches, transfer the mixture to a blender and puree until smooth, or use a hand blender. Strain the puree through a fine sieve into a pot. Discard the solids.
Heat the bisque over medium heat. Whisk in the remaining 1/4 cup butter, the remaining two tablespoons of sherry, the cream, the lemon juice, and the cayenne. Season with salt and pepper to taste.
Divide among the soup bowls and serve immediately. This bisque is especially good sprinkled with crusty croutons.