- Set a large heavy pot, preferably a cast-iron Dutch oven, over medium-high heat. Add 2 tablespoons oil and the sausage and/or ham. Cook the meat until it is lightly browned and the fat has rendered out, about 6 minutes.
- Add the onions and cook, stirring frequently, until they develop a rich caramel color, about 8 minutes.
- Add the bell pepper and the celery and continue cooking until the vegetables have softened, about 4 minutes.
- Add the garlic and the chicken, stir thoroughly, and cook until the garlic is fragrant, about 3 minutes.
- Add the tomatoes and the broth; stir thoroughly.
- Add the contents of the package. Stir thoroughly. Bring the mixture to a simmer, cover, reduce heat to low, and cook for 30 minutes. If using shrimp, place them on top of the jambalaya in the pot when 5 minutes of cooking time remains.
- Remove the jambalaya from the heat and let stand for 5 minutes. Stir. Garnish with green onions if desired.