In a medium stock pot, bring the chicken stock and half & half to a boil. Be careful, as the milk will boil over quickly!
Slowly pour in the polenta or corn meal in a gradual steady stream all the while whisking until all the polenta in poured in. Whisk in the Parmesan cheese. Add a pinch of salt and pepper and the parsley.
Reduce heat to medium and simmer for 20-30 minutes, stirring frequently to avoid clumping and burning. Stir in the butter after just before removing from the heat.