Heat the olive oil in a large skillet or Dutch oven over medium-high heat.
Add the sliced smoked sausage to the skillet and cook until lightly browned on both sides, about 3 to 4 minutes. Remove the sausage and set it aside, leaving any rendered fat in the pan.
Add the chopped onion and bell pepper to the skillet. Cook until softened, about 5 minutes.
Add the minced garlic and cook for 1 minute until fragrant.
Stir in the uncooked rice, Cajun seasoning, thyme, and black pepper. Cook for 1 minute, stirring constantly to coat the rice.
Pour in the chicken broth. Bring the mixture to a boil, then reduce the heat to low, cover the skillet tightly, and simmer for 15 to 20 minutes, or until the liquid is absorbed and the rice is tender. Do not lift the lid during this time.
Remove the skillet from the heat. Stir the cooked sausage back into the rice mixture.
If using cheese, sprinkle it over the top, cover the skillet again, and let it sit for 5 minutes to melt.
Fluff the rice gently with a fork. Garnish with fresh parsley before serving.
Notes
You can substitute smoked sausage with beef sausage or andouille sausage for a spicier flavor.
For a richer flavor, use low-sodium chicken broth.
If you prefer a creamier texture, stir in 1/4 cup of cream cheese or heavy cream with the sausage in the final step.