1. Bring water to a rapid boil in a heavy saucepot. Whisk in cornmeal in a steady stream. Lower heat to very low.
2. Cook, stirring with a wooden spoon, for 20 minutes, until polenta has reached its full thickness (it should be as thick as oatmeal, and a wooden spoon should stand upright for a few seconds when placed in the center of the pot) and is smooth. Beware: Polenta is like molten lava at this point and can splash.
3. Season with salt and pepper. Stir in the butter and cheese. Polenta will become thicker as it cools. Portion onto plates or serving platter and top with garnish of your choice.