Rinse the rice under cold water until the water runs clear. Drain and set aside.
In a large skillet or Dutch oven, heat olive oil over medium heat. Add the diced onions, bell pepper, and celery. Sauté until the vegetables are softened, about 5-7 minutes.
Add the minced garlic to the skillet and cook for an additional minute until fragrant.
Stir in the ground beef or chicken, breaking it apart with a spatula. Cook until browned, about 5-8 minutes, then drain excess fat if necessary.
Mix in the Cajun seasoning, dried thyme, smoked paprika, cayenne pepper, salt, and pepper. Stir well to combine all the flavors.
Add the rinsed rice to the skillet, stirring to coat it with the meat and vegetables.
Pour in the chicken broth and bring the mixture to a boil. Once boiling, reduce the heat to low and cover the skillet.
Simmer for 20-25 minutes, or until the rice is tender and has absorbed the liquid. Stir occasionally to prevent sticking.
In the last 5 minutes of cooking, fold in the frozen peas and cover again until heated through.
Once finished, fluff the rice with a fork and adjust seasoning if necessary.
Serve hot, garnished with sliced green onions.
Notes
Adjust the cayenne pepper to taste for desired spiciness.