Heat 1 tablespoon of oil in a large skillet over medium-high heat.
Season shrimp with salt, pepper, and 1 teaspoon of Cajun seasoning; sear until pink for 2 to 3 minutes, then remove and set aside.
Add the remaining oil to the skillet and saute the onion, bell pepper, and celery until softened, approximately 5 minutes.
Stir in the minced garlic and cook for 1 minute until fragrant.
Add the uncooked rice, remaining Cajun seasoning, thyme, and cayenne, stirring to toast the rice for 2 minutes.
Pour in the chicken broth and bring the mixture to a boil.
Reduce heat to low, cover, and simmer for 18 to 20 minutes until the liquid is fully absorbed and the rice is tender.
Fold the cooked shrimp back into the rice skillet and heat through for 1 to 2 minutes.
Garnish with chopped parsley and sliced green onions before serving.