Heat your Dutch oven over medium-high heat. Add the sliced andouille sausage and cook until browned on both sides, about 5-7 minutes. The goal here is to render out some of that flavorful fat and get those delicious caramelized edges. Transfer the sausage to a plate and set aside.
Add the vegetable oil or bacon fat to the pot. Once hot, add the holy trinity: onion, bell pepper, and celery. Cook until softened, about 5 minutes, stirring occasionally.
Toss in the garlic, bay leaves, Cajun seasoning, thyme, smoked paprika, and cayenne pepper. Cook for an additional minute until the spices become fragrant. Your kitchen should be smelling amazing right about now.
Add the diced tomatoes (with their juice) and stir to combine, scraping up any browned bits from the bottom of the pot. Those bits are flavor gold!
Return the browned sausage to the pot along with the rinsed rice. Stir to coat the rice with all those delicious flavors.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce the heat to low, cover, and simmer for about 20 minutes, or until the rice is almost tender.
If using okra, add it now and continue to cook for 5 minutes.
If you're adding shrimp, gently stir them into the jambalaya. They'll cook quickly in the hot rice mixture, about 3-5 minutes until they turn pink and opaque.
Remove from heat and let stand, covered, for 5 minutes to allow any remaining liquid to be absorbed and the flavors to meld.
Fluff the jambalaya with a fork and remove the bay leaves. Stir in the sliced green onions and chopped parsley.
Taste and adjust seasonings with salt, pepper, and hot sauce as needed.
Serve hot with additional hot sauce on the side for those who like it spicy!