Heat olive oil in a large skillet or Dutch oven over medium heat. Add the chopped onions, bell pepper, and celery. Sauté for about 5 minutes, until the vegetables are soft.
Stir in the garlic and cook for an additional 1 minute until fragrant.
Add the rice to the vegetable mixture and stir for about 2 minutes, allowing the rice to absorb some flavors.
Pour in the diced tomatoes with their juice, chicken broth, Cajun seasoning, dried thyme, cayenne pepper, salt, and pepper. Stir well to combine.
Bring the mixture to a boil, then reduce the heat to low. Cover and let it simmer for about 20 minutes, or until the rice is tender and has absorbed most of the liquid.
Once the rice is cooked, gently fold in the shrimp. Cover again and cook for an additional 5 minutes, or until the shrimp are pink and cooked through.
Remove from heat and let it sit for a few minutes. Serve hot, garnished with chopped green onions and parsley.