Chop the onion, green pepper, celery, garlic, and tomatoes and set aside separately—this is your foundation for building flavor. Peel and devein the shrimp if not already done, cut the chicken into 1-inch cubes, and slice the andouille sausage. In a small bowl, combine the shrimp and chicken with 1 tablespoon of the Creole seasoning, tossing gently to coat evenly. This early seasoning helps the proteins absorb flavor as they wait to cook.
Heat the olive oil in a large, heavy-bottomed pot or deep skillet over medium-high heat. Once shimmering, add the chopped onion, green pepper, and celery (this trio is called the Holy Trinity in Creole cooking) and sauté for 3-4 minutes, stirring occasionally, until the vegetables begin to soften and release their aromatics. This is where the dish's flavor foundation begins to develop.
Add the minced garlic and cook for 30 seconds until fragrant, then stir in the chopped tomatoes, bay leaves, thyme, smoked paprika, Worcestershire sauce, and hot sauce. Simmer this mixture for 2-3 minutes to meld the flavors together and allow the tomatoes to break down slightly. I prefer adding the hot sauce here rather than at the end because it infuses throughout the entire dish rather than just sitting on top.
Stir in the long-grain white rice, making sure it's well coated with the aromatic mixture, then pour in the chicken broth. Increase heat to bring the liquid to a boil, then reduce heat to medium and simmer uncovered for 15-18 minutes until most of the liquid is absorbed and the rice is nearly tender but still has a slight bite. Stir occasionally to prevent sticking. The rice should be about 80% cooked at this point since the proteins will finish cooking in the next step.
Add the seasoned shrimp and chicken from Step 1 along with the sliced andouille sausage to the pot, stirring gently to distribute them evenly throughout the rice. Cook over medium heat for 8-10 minutes, stirring occasionally, until the shrimp are pink and firm and the chicken is cooked through. I like to let the sausage cook slightly longer than the shrimp and chicken to allow its smoky flavors to fully infuse into the jambalaya. Taste and adjust seasoning with additional salt, pepper, and Creole seasoning as needed. Remove the bay leaves before serving.