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. Sprinkle the green onions on top.