In a saucepan (about 3 Qt) over medium-high heat, bring the broth and milk to a boil. Gradually and slowly stir in the stone-ground polenta or yellow cornmeal. I use a whisk and stir constantly while adding the polenta to prevent lumps forming.
Cook, stirring frequently until the polenta thickens and starts to bubble up and spit. Immediately, lower the heat (if you have an electric stove, you may need to remove the pot from the burner for about 40 seconds as the heat lowers gradually and slowly).
Continue cooking and stirring frequently with a wooden spoon or spatula scraping the bottom of the pot to prevent the polenta from scorching. Simmer for about 40 to 45 minutes or until the polenta is thick, tender and pulls away from the sides of the pan when stirring.
Add the butter and Parmesan cheese and stir until well combined. Season to taste and serve immediately.
If the polenta thickens too much, becomes firm or sets, whisk in additional broth or milk. For a richer consistency, you can add a big splash of half and half or heavy cream and extra butter.