In a large saucepan over medium heat, add the polenta, breaking it up as much as possible using a potato masher, wooden spoon, or whisk.
Pour in the milk and bring the mixture to a simmer. Whisk occasionally, until the polenta and milk have come together and are totally smooth.
Add in 1/3 of the cheese and stir until totally melted and combined. Repeat twice to incorporate the rest of the cheese.
Remove from the heat. Season with the pepper and stir in the butter. Add more milk if the mixture is too thick after sitting for a few minutes, and serve.