A good recipe for Brunswick stew is Bob Garner's recipe from his book, "North Carolina Barbecue." The recipe, located on FoodNetwork.com, involves cooking a chicken with water in a Dutch oven, adding several types of vegetables to the remaining liquid and cooking the stew until finished.
Cut a 3 1/2 pound chicken into pieces and boil it in 2 quarts of water in a Dutch oven. Once brought to a boil, reduce the heat and simmer for 40 minutes. Remove the chicken pieces from the Dutch oven and set them aside, leaving 3 cups of broth in the pot. Pour the liquid from one can of baby lima beans into the pot and set the beans aside. Add two 28-ounce cans of chopped tomatoes to the pot, and bring it back to a boil over medium-high heat. Continue to cook for 40 minutes.
While the stew is cooking, remove all the meat from the chicken pieces and shred it. Mash the canned baby lima beans and add them to the stew along with the chicken meat, a 16-ounce package of frozen baby lima beans, 3 medium peeled and diced potatoes, and 1 large diced onion. Cook for three hours and 30 minutes, then add two 15-ounce cans of creamed corn and continue to cook over low heat for one hour, stirring often.
To finish, add 1/4 cup of unsalted butter and season with salt, pepper, sugar and hot sauce to taste.