Preheat your oven to 375°F (190°C).
In a medium saucepan, bring the chicken broth to a boil. Stir in the rice and return to a boil, then reduce the heat to low, cover, and simmer for about 15 minutes, until the rice is tender and the liquid is absorbed.
While the rice is cooking, heat the olive oil in a large skillet over medium heat. Add the sausage and cook until browned, about 5 minutes.
Add the onion, bell pepper, celery, and garlic to the skillet. Cook until the vegetables are softened, about 5 minutes.
Stir the diced tomatoes, Cajun seasoning, paprika, thyme, and cayenne pepper into the sausage and vegetable mixture. Season with salt and pepper to taste.
In a large casserole dish, combine the cooked rice with the sausage mixture. Mix well to combine.
Sprinkle the shredded Cheddar cheese evenly over the top of the casserole.
Bake in the preheated oven for about 20 minutes, or until the cheese is melted and bubbly.
Garnish with chopped parsley before serving.