1. Combine the cold water and the polenta in a heavy-bottomed pot. Turn the heat on low. Stir occasionally with a wooden spoon, scraping the bottom of the pot. Gradually the polenta will start to thicken. Keep cooking and stirring. Taste the polenta. If it seems grainy, cook it longer. You may need to add a bit more water. Just wait until the polenta is thick and doesn't feel grainy on your tongue. This may take 30 minutes.
2. Stir in the grated cheese and the olive oil or butter. Season with salt to taste.
Serve the polenta as is. Or pour the polenta into a double boiler and keep warm, adding water or stock as needed to keep it soft.
Or pour the polenta onto oiled baking sheets. Refrigerate and cover with plastic wrap after the polenta firms up. Cut it into strips or triangles and then you may fry the polenta in oil or butter, or you may place it in oiled baking gratin dishes, sprinkle with parmesan and heat in a moderate oven.Serving Size: 1/2 cup