Heat the vegetable oil in a large skillet over medium heat. Add the diced onions, bell peppers, and celery. Sauté for about 5 minutes until the vegetables are softened.
Add the minced garlic to the skillet, and cook for an additional minute until fragrant.
Add the ground beef (or pork) to the skillet. Break it up with a wooden spoon and cook until browned and fully cooked, about 5-7 minutes. Drain excess fat if necessary.
Stir in the Cajun seasoning, paprika, cayenne pepper, black pepper, and salt. Mix thoroughly to coat the meat and vegetables with the spices.
Add the uncooked rice to the skillet, stirring until the rice is well combined with the meat mixture.
Pour in the chicken broth (or water) and bring the mixture to a boil.
Once boiling, reduce the heat to low, cover the skillet, and simmer for approximately 20 minutes or until the rice is tender and has absorbed most of the liquid.
Remove the skillet from heat and let it sit for a few minutes before uncovering. Fluff the rice with a fork.
Serve the dirty rice hot, garnished with sliced green onions, and optional hot sauce on the side.