In a medium stock pot, combine the reserved shrimp shells, 1/2 onion, 1 carrot, 2 strips celery, and 4 cups water. Simmer for 1 hour, uncovered; stirring occasionally. Strain the stock into a smaller saucepan, boil and reduce the stock to 2 cups.
Remove from heat.
In a heavy skillet, melt grease over medium heat.
Add the onions, celery, garlic and green bell pepper; saute until soft and beginning to caramelize around the edges.
Add the bay leaves, salt, black pepper, brown sugar, cayenne pepper, hot sauce, and 2 cups reduced shrimp stock. Bring to a boil and add crushed rosemary, crushed thyme, crushed basil, tomatoes, and tomato sauce.
Cover and simmer over low/medium heat, stirring occasionally, for 1 hour.
Add the cleaned and deveined shrimp. Stir, cover and turn off the heat.
Let the shrimp sit for 15 to 20 minutes or until pink throughout.