Combine the water, salt and butter in a medium saucepan and bring to a boil. Gradually add the polenta or cornmeal, whisking constantly so it doesn't lump. Lower the heat and continue cooking, stirring frequently, until quite thick, 10-15 minutes. Remove from heat and stir in the parmesan cheese and cayenne.
Line a 9 inch pie plate with plastic wrap, letting it extend over the edges. Spread the polenta evenly over the plastic wrap and smooth the top with a spoon. Cover tightly with plastic wrap and chill until firm, at least 1 hour.
Prepare a fire in a grill. Position the oiled grill rack 4-6 inches above the fire. Invert the pie plate to unmold the polenta. Peel off the plastic wrap. Cut the polenta into 6 pie-shaped wedges. Brush each wedge lightly on both sides with oil. Arrange the polenta wedges on the rack. Grill, turning two or three times, until golden, about 10 minutes.
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