Add water and cornmeal to cooking pot. Bring to a boil and then reduce heat to simmer stirring frequently. After about 30 minutes the mixture will become quite thick. Stir in the butter and parmesan cheese. Continue to cook until the mixture is very thick and starts to come away from the side of the pot.
Pour cooked polenta evenly into parchment paper lined, 8 in square baking dish. Cover and refrigerate until well chilled (several hours) and firm.
Slice into 12 squares orwedges. Place polenta wedges on greased grill over medium heat; cook on both sides until browned. Hint: Use a non-stick, well oiled pan. Heat the oil so it is almost to smoking point. Try not to move the polenta pieces until well browned or they will stick to the surface of the pan.
Serve polenta with hot tomato sauce or other Italian food.