Rinse and drain the white rice under cool running water in a mesh strainer. Then add the drained rice to a rice cooker with 4 cups water, 3 bay leaves, 1 tablespoon chicken bouillon, and 1 teaspoon salt. Cook the rice until done. Then spread the rice on a large sheet tray in a thin layer, cover with plastic wrap, and allow to cool for approximately 2-3 hours or overnight in the refrigerator. *If you don't have a rice cooker, cook the rice per package instructions, adding bay leaves, salt, and chicken bouillon for extra flavor.
Heat griddle on medium heat to about 375-400℉.
Add the ground beef and breakfast sausage to the hot griddle, and cook until almost done, chopping and breaking the meat apart into small crumbles. Then, move to the meat to the side of the griddle.
Scrape some of the residual grease from the meat to a clear area on the griddle. Add the diced onion, diced bell pepper, diced celery, and about 1/2 of the sliced green onion to the grease and sauté for about 3-4 minutes. Then, add the vegetables to the meat mixture, stir together, and move to the side of the griddle to continue to cook.
Add about 2 tablespoons oil to a clear area on the griddle and spread it around with your spatula. Add the cooled rice and the diced Cajun sausage to the oiled griddle. The heat from the griddle will start to break the clumps of rice apart after a few minutes. Then, sauté the rice and Cajun sausage together for 2-3 minutes.
Add the chicken livers to the ground meat and vegetable mixture. Mix together well, and allow to cook for about 3-4 minutes in a thin layer. Add the minced garlic, and sauté together, cooking until the chicken livers are cooked through.
Add 2 tablespoons of flour to the ground meat and vegetable mixture. Mix well, and cook for about 2-4 minutes.
Add the meat and vegetable mixture to the rice and Cajun sausage. Mix together well. Add Cajun seasoning, thyme, oregano, cayenne pepper, parsley, and remaining green onions. Mix together so that all ingredients are fully incorporated.
*At this time, you may add up to 1 cup of chicken stock to the dirty rice, if needed. This is really a matter of personal preference, but I wanted my rice to be more moist, so I added the full cup.
Transfer dirty rice to a serving platter. Serve with hot sauce, additional sliced green onions for garnish, or your favorite Cajun toppings.