In a 3-quart pan over high heat, bring 4 cups water to a boil. Reduce heat to a low boil.
Stirring constantly, pour in polenta in a slow, thin stream, pausing occasionally to break up any lumps. Stir in 1/2 teaspoon salt.
Reduce heat and simmer, stirring often, until polenta is thick and creamy to bite and pulls away slightly from sides of pan when stirred, 20 to 40 minutes (see notes); adjust heat as necessary to maintain a simmer. Stir in butter, if desired, and add more salt to taste.