In a medium heavy-bottomed saucepan over high heat, bring the water to a boil. Stir in the kosher salt.
Slowly pour the cornmeal into the boiling water in a thin stream while whisking constantly to prevent lumps.
Once all the cornmeal has been added and the mixture begins to thicken slightly, switch to a wooden spoon or heatproof spatula. Reduce the heat to low.
Cook the polenta over low heat for about 45 minutes, stirring every 10 minutes. Keep the heat low enough to prevent splattering while allowing the mixture to gently bubble.
If the polenta becomes too thick or difficult to stir, add ½ cup of water and stir to loosen. You can add up to 1 cup additional water total to maintain a smooth, creamy consistency.1
To check for doneness, spoon a small amount onto a plate and let it cool slightly. The grains should be tender with no gritty texture.
Season with additional kosher salt and freshly ground black pepper to taste.
Stir in the butter until completely melted and incorporated. The polenta should be smooth, rich, and creamy.
Serve immediately, topped with grated Parmesan cheese if desired.
If not serving right away, place the saucepan into a larger pot of barely simmering water or transfer the polenta to a double boiler. Cover and keep warm over low heat for up to 1 hour, stirring occasionally.