In a medium-sized, heavy-bottomed saucepan, bring 4 cups of water to a rolling boil over high heat.
Reduce the heat to low to achieve a gentle simmer and slowly whisk in 1 cup of polenta in a thin, steady stream to prevent lumps from forming.
Add 1 teaspoon of salt and cook the polenta, stirring frequently with a wooden spoon for 25 to 30 minutes, until the grains are tender and the mixture has thickened significantly.
Pour in 1/2 cup of whole milk and stir continuously for 2 to 3 minutes until the milk is fully incorporated and the polenta is creamy.
Remove the saucepan from the heat and stir in 4 tablespoons of butter and 1/2 cup of grated Parmesan cheese until the butter has melted and the cheese is completely blended in. Season with black pepper to taste and serve immediately.
Notes
Use coarse-ground polenta for the best texture. Stir frequently to prevent lumps.