Over medium high heat, melt the butter in a heavy, nonreactive 6-quart saucepan or Dutch oven.

​Add the sausage and pickled pork or ham and cook until all of the fat is rendered out of the meats, about five minutes, stirring occasionally.

Add the yellow onions, the white part of the green onions and the sweet peppers. Cook the vegetables until they are clear, about five minutes, occasionally stirring and scraping the  pan bottom clean.

Add the crushed tomatoes, tomato puree, garlic, bay leaf, salt, black and cayenne pepper, and thyme. Cook and stir this base sauce about two minutes. (If the dish is being prepared ahead, allow the base sauce to cool, then place in a lidded nonreactive container and store it in the refrigerator for up to two days. For the final preparation, heat the base to a boil and proceed with the remainder of the recipe.)

Add the chicken stock and pepper sauce to the base and bring to a boil.

Reduce the heat to maintain a strong simmer, and simmer the liquid uncovered until it is reduced by one third, about one hour 15 minutes. Skim any foam or coagulates as they develop on the surface.

Return the liquid to a boil and stir in the rice.

Reduce the heat to medium, and cook uncovered until the rice is just short of being done (it should still be a little firm in the center), about 25 minutes, stirring occasionally.

Add the shrimp and cook until the rice is tender and the shrimp turn bright pink, about three minutes. Do not overcook.

Stir in the green part of the green onions and serve at once.