In a large pot or Dutch oven, heat a tablespoon of oil over medium heat. Add sliced andouille sausage and brown it until it develops a nice color. Remove the sausage from the pot and set it aside.

In the same pot, add diced onions, bell peppers, and celery. Sauté until the vegetables are softened, then add minced garlic. Cook for an additional minute until the garlic becomes fragrant.

Stir in the long-grain white rice, ensuring it's well-coated with the vegetable mixture.

Add the diced tomatoes, chicken broth, paprika, dried thyme, dried oregano, cayenne pepper, salt, and black pepper. Mix well.

Bring the mixture to a boil, then reduce the heat to low. Cover the pot and let it simmer for about 20-25 minutes or until the rice is tender and has absorbed the flavors.

Once the rice is cooked, add the browned andouille sausage back to the pot. Stir to combine and let it heat through.

Adjust the seasoning if needed. Garnish with chopped green onions and parsley before serving.

Serve the Sausage Jambalaya hot, and enjoy the hearty and flavorful dish!