Heat the olive oil in your skillet or Dutch oven over medium heat. Add the sliced chicken sausage and cook until browned on both sides, about 5-7 minutes. Remove the sausage from the pan and set aside.
In the same pan, add the diced onion, green bell pepper, and celery. Sauté for about 5 minutes until softened and fragrant. Stir in the minced garlic and cook for another minute, being careful not to burn the garlic.
Pour the undrained diced tomatoes into the pan along with the Cajun seasoning, dried thyme, black pepper, and cayenne pepper if using. Stir and let the spices bloom for about 2 minutes.
Add the long-grain rice to the pan and stir well to coat the grains. Pour in the chicken broth and bring the mixture to a gentle boil.
Return the browned chicken sausage to the pan, nestling it into the rice mixture. Reduce heat to low, cover with a lid, and simmer for 20-25 minutes until liquid is absorbed and rice is tender.
Turn off the heat and let the jambalaya rest covered for 5 minutes. Fluff the rice with a fork and garnish with sliced green onions and chopped fresh parsley before serving.