Bring 2 quarts lightly salted water to a boil in a large pot. Add the polenta in a fine stream all at once. Stir until it thickens. Each polenta absorbs water differently, so have a pot of boiling water ready to add, if the polenta becomes too thick. At the end of the cooking time, which can take 30 minutes, stirring all the time, add the Parmesan, butter and some ground nutmeg. Serve the polenta hot like a purÄe. Or pour it into a sheet pan and smooth it out to 1/2-inch thick. When it is cold, cut into squares or triangles and brown it on both sides in half butter, half oil.
