In a large pot, bring 5 cups water and the milk to a gentle boil. Add the polenta, along with a good amount of salt and pepper, and stir constantly for about 5 minutes.
Turn the heat down to low, partially cover the pot and allow the polenta to simmer for about 20 minutes, giving it a stir every 5 minutes; depending on the size of your polenta or cornmeal, it may take more or less cooking time to become creamy.
Turn the heat off, add the butter and cheese and give everything a good stir until the butter and cheese melt. Keep in mind that polenta hardens as it sits, so eat up!