Place chicken or turkey giblets, except the liver in a saucepan. Add water just to cover giblets and salt lightly. Add a few celery leaves and onion slices to the water. Cover and simmer for 1 to 2 hours. Add the liver and continue to simmer for 5 to 10 more minutes. Cool the giblets in the broth and then remove the giblets and chop into small pieces.
Remove your chicken or turkey to a hot platter and keep warm. Leave the small crusty pieces in your roasting pan. Pour the meat juices and fat into a large measuring cup. Skim off the fat, reserving 3 to 4 tablespoons. For 2 cups of gravy, return reserved fat to the pan. Stir in ΒΌ cup all purpose flour. Blend together the reserved fat and the flour. Cook and stir gravy over low heat until mixture is thickened and bubbly.
Remove the pan from the heat. Add 2 cups of the meat juices and giblet broth all at once. Blend thoroughly. Add the chopped giblets. Season to taste with salt and pepper. Simmer, stirring constantly for 2 to 3 minutes.
Makes 6 to 8 servings.