Add about 1/2 cup of the milk or cream to the pot and turn down the heat allowing the grits to simmer another ten minutes or so. As the liquid cooks off or is absorbed, add more cream or milk, cooking the grits until the desired consistency is reached, a total cooking time of at least an hour.
The grits should be piping hot when served; slightly soupy but full-bodied enough that they do not run on the plate.