- For the crawfish: In a large stockpot over medium high heat, boil all ingredients for 4 minutes, until crawfish are cooked. Remove from heat and cool. Drain crawfish. Discard stock or save for future use. Remove tail meat from crawfish, reserving both meat and shells.
- For the bisque: In a large stainless steel soup pot over medium heat, melt 4 tablespoons of butter. Add shallots and onions and sauté for 5 minutes, stirring occasionally. Add crawfish shells and sweat for a few minutes. Add water, tomato paste, carrots, cognac, cayenne, black pepper, and salt and simmer, covered, for 20 minutes, stirring occasionally. Stir in cream and simmer for 30 minutes, uncovered, stirring occasionally. Strain into clean pot and keep warm over low heat. Season to taste. Discard solids.
- To serve: In a sauté pan over medium heat, melt remaining 4 tablespoons of butter. Heat crawfish tails until thoroughly warmed. Divide evenly among 6 soup bowls. Ladle hot bisque over crawfish and serve.