In a large Dutch oven or deep skillet, heat vegetable oil over medium-high heat.
Add the sliced andouille sausage and cook for 5-6 minutes until browned. Remove sausage with a slotted spoon and set aside.
Add the diced onion, bell pepper, and celery to the remaining fat in the pot. Sauté for 7 minutes until the vegetables are softened.
Stir in the minced garlic, Cajun seasoning, and dried thyme. Cook for 1 minute until fragrant.
Add the dry rice to the pot and stir for 2 minutes to toast the grains.
Pour in the chicken stock and Worcestershire sauce. Bring the mixture to a rolling boil.
Reduce heat to low, cover tightly, and simmer for 18-20 minutes until the rice is tender and liquid is absorbed.
While rice cooks, season shrimp with salt and pepper. In a separate skillet, sear shrimp for 2 minutes per side until opaque and pink.
Once the rice is done, fluff with a fork. Gently fold in the cooked sausage, seared shrimp, green onions, and parsley.
Cover and let the dish rest for 5 minutes before serving to allow flavors to meld.