Step 1: Heat the vegetable oil in a large Dutch oven or heavy-bottomed pot over medium-high heat.
Step 2: Add the sliced Andouille sausage and cook until browned on both sides. Remove with a slotted spoon and set aside.
Step 3: In the same pot, add the chicken pieces. Brown them thoroughly, then remove and set aside with the sausage.
Step 4: Add the onion, bell pepper, and celery to the pot. Sauté for 5-7 minutes until the vegetables are soft and the onion is translucent.
Step 5: Stir in the minced garlic, Creole seasoning, and thyme. Cook for 1 minute until fragrant.
Step 6: Add the crushed tomatoes and the browned meats (plus any juices) back into the pot. Stir to combine.
Step 7: Add the rice and stir for 1-2 minutes to coat the grains with the spice mixture.
Step 8: Pour in the chicken broth and add the bay leaves. Bring the mixture to a rolling boil.
Step 9: Reduce heat to low, cover the pot tightly, and simmer for 20-25 minutes until the rice is tender and the liquid is absorbed.
Step 10: Remove from heat, let it sit covered for 5 minutes, then fluff with a fork and garnish with green onions before serving.