In a large skillet or Dutch oven, brown the ground meat over medium heat until cooked through. Drain excess fat if necessary.
Add the chopped onion, bell pepper, celery, and garlic to the skillet. Cook until the vegetables are softened, about 5-7 minutes.
Stir in the rice, paprika, thyme, and oregano, coating the rice and vegetables evenly with the spices.
Pour in the chicken broth and bring the mixture to a boil. Reduce the heat to low, cover, and simmer for 20-25 minutes, or until the rice is cooked and most of the liquid is absorbed.
Once the rice is cooked, fluff it with a fork and taste for seasoning. Adjust salt and pepper if necessary.
Serve the Dirty Rice hot, garnished with chopped green onions, and accompanied by hot sauce for an extra kick.