Bring water to a boil in a medium sauce pan over high heat. Add 1 teaspoon salt and pour cornmeal slowly into water, stirring with a wire whisk or wooden spoon. Continue stirring as mixture thickens, 2 to 3 minutes.
Turn heat to low and cook for at least 45 minutes, stirring every 10 minutes or so. If polenta becomes too thick to stir comfortably, thin it with 1/2 cup water, stir well and continue cooking. Add up to 1 cup more water as necessary, to keep polenta soft enough to stir. Put a spoonful on a plate, let it cool, then taste. Grains should be swollen and taste cooked, not raw. Adjust salt and add pepper if you wish.
Add 6 tablespoons butter to pot and stir well. Serve immediately or transfer to a double boiler set over low heat, cover and keep warm for up to an hour or so. (Or set the saucepan in a pot of barely simmering water.) Stir well before spooning into low soup bowls. Sprinkle with Parmesan, if desired.
