Warm the olive oil in a large, heavy-bottomed pot or Dutch oven over medium heat.

Add the sliced smoked sausage and cook for 3 to 4 minutes, stirring occasionally, until lightly browned. Transfer the sausage to a plate and set aside, leaving the rendered fat in the pot.

Season the chicken thigh pieces with half of the salt and half of the black pepper. Add the chicken to the pot and cook for 4 to 5 minutes, stirring occasionally, until lightly browned on the outside. Transfer the chicken to the plate with the sausage.

Add the unsalted butter to the same pot. Once melted, stir in the chopped onion, diced green bell pepper, and diced celery.

Cook the vegetables for 5 to 6 minutes, stirring often, until they soften and the onion becomes translucent.

Stir in the minced garlic and cook for 30 seconds, just until fragrant, being careful not to let it brown.

Sprinkle in the smoked paprika, dried oregano, dried thyme, cayenne pepper, ground cumin, sweet paprika, and the remaining salt and black pepper. Stir well to coat the vegetables in the spices and cook for 1 minute to lightly toast the spices.

Add the rinsed long-grain white rice to the pot and stir for 1 to 2 minutes so the rice is well coated with the vegetable and spice mixture.

Pour in the diced tomatoes with their juices and the chicken broth, then add the hot sauce. Stir to combine, scraping up any browned bits from the bottom of the pot.

Return the browned sausage and chicken, along with any accumulated juices on the plate, back into the pot and stir gently to distribute evenly.

Bring the mixture to a gentle boil over medium-high heat, then reduce the heat to low, cover the pot with a tight-fitting lid, and simmer for 20 minutes without lifting the lid.

After 20 minutes, quickly lift the lid and scatter the peeled and deveined shrimp over the top of the rice mixture. Do not stir. Cover the pot again and continue to cook over low heat for 5 to 7 minutes, until the shrimp are pink and opaque and the rice is tender.

Remove the pot from the heat and let the jambalaya rest, covered, for 5 minutes to allow the flavors to settle and the rice to finish steaming.

Uncover the pot and gently fluff the jambalaya with a fork, folding the shrimp through the rice and distributing the meats evenly.

Sprinkle the chopped fresh parsley and sliced green onions over the top, then taste and adjust the seasoning with additional hot sauce or black pepper if desired before serving.