Bring the water to a boil in a deep heavy saucepan. Add the salt then gradually pour in the polenta, whisking constantly. Reduce heat to medium and stir constantly with a wooden spoon 25 minutes or until the polenta starts coming away from the sides of the pan.
Spoon the polenta into an oiled shallow tray. Smooth the surface with a spatula. Let cool in the fridge until set, about 2 hours.
Preheat the oven to 180 degrees C.
When set, slice the polenta into squares. Arrange the squares on a buttered baking tray. Sprinkle over the extra Parmesan. Bake in the oven for 15 minutes to heat through, then place under the grill until golden.