Stir the meal gradually with the cold water to form a smooth mixture. Slowly add it to the boiling salted water, stirring constantly to prevent lumps. If in a double boiler, cook without further stirring for three hours. If in a heavy iron pot, stir gently now and then for an hour with a wooden paddle, taking care not to disturb the crust that will form against the pot.
The polenta should be about the consistency of spoon bread when done. If too thick, add more hot water.
Stir in the cubed cheese at the last if desired. Then shape into a mound and cover with grated cheese, to be served separately with whatever sauce is desired. Or make into a ring around the sauce on one plate.