In a medium pot, bring 4 ½ cups of water to a boil.
Pour the cornmeal into the boiling water in a thin stream, whisking as you pour to prevent big clumps from forming.
Reduce the heat to a simmer and cook for about 15 minutes, stirring frequently.
Sprinkle in about a teaspoon of salt as you cook.
Add a couple of teaspoons of water here and there as needed if the polenta seems too thick.
Stir in the butter and goat cheese until the cheese has completely melted, and serve.
