In a large skillet or frying pan, heat the olive oil over medium heat.
Add the sliced Andouille sausage and cook until browned and slightly crispy, about 5-7 minutes. Remove the sausage from the pan and set aside.
In the same pan, add the diced onion and bell pepper. Sauté for about 4-5 minutes until they become tender. Add the minced garlic and sauté for an additional minute until fragrant.
Stir in the rice and cook for about 2 minutes, allowing it to toast slightly with the vegetables.
Pour in the diced tomatoes with their juices, chicken broth, Cajun seasoning, thyme, and bay leaf. Stir everything together, bringing the mixture to a gentle boil.
Reduce the heat to low and return the sausage back to the pan. Cover with a lid and let it simmer for 18-20 minutes, or until the rice is tender and has absorbed most of the liquid.
Once the rice is cooked, stir in the frozen peas and let it sit covered for another 5 minutes to allow the peas to heat through.
Remove the bay leaf, and season the dish with salt and pepper to taste. Fluff the rice with a fork before serving.
Garnish with freshly chopped parsley for a pop of color and extra flavor.