Place chicken stock and milk in large sauce pan. Season with salt and pepper. Add grits to liquid and let sit 5 minutes or longer. Turn heat on to moderately high and bring to a simmer. Once the liquid bubbles, reduce heat to very low and continue to cook, stirring occasionally, for about 45 to 60 minutes, until liquid is mostly absorbed.
Stir in butter, cheese and heavy cream. Adjust seasoning.