Brown the Sausage: Heat the oil in a large Dutch oven or heavy-bottomed pot over medium-high heat. Add the sausage slices and cook them, stirring occasionally, until they develop a deep brown color and release their flavorful oils, about 5 to 7 minutes. Using a slotted spoon, transfer the sausage to a plate and set aside, leaving the rendered fat in the pot.
Sauté the Vegetables: Add the chopped onion, bell pepper, and celery to the pot. Stir frequently and cook until the vegetables soften and become fragrant, about 5 minutes. Add the minced garlic and cook for an additional minute, being careful not to burn it.
Build the Flavor Base: Pour in the chicken broth, crushed tomatoes, and diced tomatoes with their juices. Sprinkle in the Creole seasoning and stir well to combine all the ingredients. Bring the mixture to a rolling boil.
Add Rice and Sausage: Stir in the rice along with the browned sausage. Reduce the heat to low, cover the pot, and let it simmer gently for about 20 minutes. Stir occasionally to prevent sticking and check the rice for tenderness.
Cook the Shrimp: Once the rice is tender, nestle the shrimp into the pot, then cover again. Let the shrimp cook through until they turn pink and opaque, about 3 to 5 minutes.
Rest and Serve: Remove the pot from heat and allow the jambalaya to rest covered for 5 minutes. This helps the flavors meld and the rice finish cooking perfectly. Stir gently before serving, and garnish with sliced green onions if desired.