Combine seasoning mix ingredients in a small bowl and set aside.
In a large stock pot or dutch oven, melt the chicken fat over medium heat. Add 1 1/2 cups onions, 1 cup of celery,and 3/4 cup green bell peppers. Cook until the vegetables are caramelized, about 20 minutes, stirring occasionally. The onions should be a rich dark brown, but not burnt.
Add the hame, sausage and remaining onion, celery and green bell peppers. Continue cooking and stirring for 5 minutes. Add the tomatoes, garlic, tomato sauce, bay leaves, seasoning mix and Tabasco. Simmer for 15 minutes, stirring occasionally.
Turn the heat to high, fold in rice until well mixed. Add the stock, cover pot and remove from heat. Let stand, covered, for 15 minutes. Return to medium heat and cook, covered, until rice is tender, about 10 minutes.