Along with gumbo and crawfish etoufee, shrimp Creole is a favorite Louisiana dish. This tomato-based shrimp dish is slightly lighter fare because it does not have to be made with a roux (a fat and flour mix used to make gravy bases). It is also slightly easier to make than some Louisiana recipes, because it doesn't have to be overseen and stirred as much some dishes.
Heat the butter on medium-high heat, and stir in the chopped vegetables. Allow the vegetables to cook until they become tender.
Add the tomato sauce and stewed tomatoes. Allow the sauce to come to a boil for approximately five minutes and then reduce the heat to medium.
Add the four cups of broth and the Tabasco. Raise the heat to high and allow the mixture to come to a rolling boil for 15 minutes.
Stir in the two pounds of shrimp, allowing the shrimp to mix thoroughly with the sauce and vegetable mix. Reduce the heat to low.
Allow the shrimp Creole to simmer for 10 minutes or until the shrimp turn orange-pink in color. Remove the dish from heat and serve it over steamed rice.