Twist off the tails, remove the veins and wash out the heads. Remove the meat from one tail, cut it into 1-in. cubes, and set aside to use later as garnish. Chop remaining tail and carapaces into large chunks.
Place a large saucepan on high heat and melt the butter. Add the onion, carrots and garlic. Cook while stirring until the onions turn translucent. Add the chopped lobster chunks, tomato paste, brandy, sweet white wine, chopped tomatoes, thyme, cayenne pepper and salt. Stir well and add the fish stock.
Add the cream to the saucepan and allow to simmer over low heat for approximately 1 hour, and strain the broth into another saucepan (be sure to press and strain as much liquid from the lobster chunks as possible before discarding them). Whisk the strained soup vigorously until it is lightly frothy.
Ladle the soup into a serving bowl. Garnish with a few sprigs of Italian flat leaf parsley and cubes of lobster tail meat. Enjoy this elegant chowder with your dining partner on a rainy winter’s day along with a loaf of warm sourdough bread and a couple of your favorite beverages.