Add the chicken broth and milk to a large saucepan and bring it to a simmer over medium heat.
Add the polenta cornmeal grounds, then let simmer for 25-35 minutes. Make sure it doesn’t come to a boil. Lightly whisk (or stir with a wooden spoon) every few minutes.
Add the butter and Parmesan, stirring continuously to fully melt the cheese and avoid lumps.
Season with salt and pepper to taste, then serve while hot!