Don't let the name keep you from trying this savory Louisiana classic. Dirty Rice is generally served as a side dish, but is fairly substantial and would make a satisfying main course for lunch or a light supper.
In a medium saucepan, bring the gizzards, chicken broth, and water to a boil. Reduce the heat to medium-low, cover, and simmer until the gizzards are tender, about 45 minutes. Reserving the broth, remove the gizzards, and when they are cool enough to handle, mince them and set them aside.
In a Dutch oven or flameproof casserole, cook the bacon over medium heat until crisp, about 10 minutes. Reserving the fat in the pan, drain the bacon on paper towels; crumble and set aside.
In the bacon fat, saute the gizzards over medium heat until browned, about 5 minutes.
Add the green and red bell peppers, the onion, scallions, carrots, parsley, garlic, salt, pepper, and cayenne. Cook over medium heat until vegetables have softened, about 5 minutes.
Add the rice and reserved broth. Increase the heat to medium-high and bring to a boil. Stir once, reduce heat to medium-low, cover, and simmer until the rice is tender, about 15 to 20 minutes.
Meanwhile, in a medium skillet, melt the butter over medium heat. Add the chicken livers and saute until firm, about 5 minutes. Let the livers cool slightly, then coarsely chop them. Toss the chicken livers and bacon with the rice. Cover and let sit for 10 minutes before serving.