1. Put water, grits and salt in a heavy saucepan. Bring mixture to the boil and cook, stirring almost constantly, until the raw taste of the grits has mellowed, 30—40 minutes. Cut the butter into pieces and add to the grits, beating until the butter is melted and mixed in.
2. Scrape the grits into a lightly buttered loaf tin. Chill.
3. Cut a loaf of grits into 2-cm/3/4-in slices. Lightly brush all the edges with olive oil. If you have seasoned olive oil, or have time to let some garlic and rosemary sit in it ahead of time, that's even better.
4. Put the oiled slices on the barbecue grill when the flames have died to a glow and the coals are covered with white ash. Cook for 4—5 minutes, until the underside is seared in the spots where it touches the grill and lightly browned elsewhere. Turn. Sprinkle the top with Parmesan cheese and cook for another 4 - 5 minutes.