In a large pot, bring chicken broth to a boil then stir in polenta. Keeping stirring, scrapping along the bottom and breaking up any bits. Reduce to rolling simmer and let cook for about 40-45 minutes, stirring and scraping bottom and sides of pot every 5-10 minutes to prevent sticking.
Taste the polenta, it should have a slightly gritty texture but be soft and not have a raw taste. Add shredded cheese one cup at a time, stirring until melted. Add salt and pepper and stir again. Taste again and add more seasoning if needed.
Serve polenta warm and topped with extra cheese. As polenta cools, it will begin to set. Reheat and stir in a tablespoon of water at a time as needed until desired consistency is reached.