Slice the sausage into 1/4-inch rounds and heat a large pot over medium heat.
Add the sausage to the pot and cook for about 5-7 minutes until browned.
Add in the diced onion, bell pepper, celery, and minced garlic. Sauté for 5 minutes.
Stir in the rice, mixing well with the vegetables and sausage.
Pour in the chicken broth and add the diced tomatoes, Cajun seasoning, and thyme.
Bring the mixture to a boil, then reduce the heat and cover the pot.
Cook for about 20-25 minutes, or until the rice is tender and liquid is absorbed.
Remove from heat and let it sit, covered, for 5-10 minutes before serving.
Fluff the jambalaya with a fork and sprinkle with chopped green onions before serving.