In a medium heavy-bottomed saucepan over high heat, bring water to a boil. Stir in the kosher salt.
Slowly pour the cornmeal into the water in a thin stream, whisking constantly with a wire whisk to prevent lumps.
Once all the cornmeal is added and the mixture begins to thicken slightly, switch to a wooden spoon or heatproof spatula. Reduce the heat to low.
Continue cooking the polenta over low heat for at least 45 minutes, stirring every 10 minutes. Keep the heat low enough to prevent splattering, but high enough that the polenta gently bubbles.
If the polenta becomes very thick or difficult to stir, add ½ cup of water and stir to loosen. You can add up to 1 cup additional water total, as needed, to maintain a smooth, creamy texture.
To test doneness, spoon a little onto a plate and let it cool. Taste it; the grains should be fully cooked and tender, with no raw or gritty texture.
Season with more kosher salt and freshly ground black pepper to taste.
Stir in the unsalted butter until fully melted and incorporated. The polenta should now be smooth, rich, and creamy.
Serve immediately. If desired, sprinkle with grated Parmesan cheese.
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.