If you cannot find or do not want to add chicken gizzards, omit and add 12 ounces coarsely chopped mushrooms with the onions, celery, and pepper. To omit the liver as well, use 12 ounces mushrooms and 1 pound ground pork, sausage, or tasso ham.
Prepare for cooking and pat dry:
Heat in a Dutch oven or large saucepan over medium heat:
Add the gizzards and brown on all sides, about 10 minutes. Transfer to a plate. Add to the pot and brown, turning once, about 8 minutes:
Set aside with the cooked gizzards. Add to the pot:
Break up the meat with a spoon, and cook until browned, about 6 minutes. Stir in:
Cook until softened, about 5 minutes, scraping any browned bits off the bottom of the pot.
Finely chop the gizzards and liver and return them to the pot, along with:
Cook, stirring occasionally, for another 3 minutes. Add:
Stir, bring to a boil, then reduce the heat to medium-low, cover, and simmer until the rice is tender and the liquid is absorbed, about 15 minutes. Let stand off the heat for 5 minutes. Stir in:
Serve with: