Bring 6 cups water and the chicken broth to a boil in a 4-quart saucepan. Add the salt, and then add the polenta in a slow stream while whisking constantly. Lower the heat to medium-low and cook, stirring with the whisk, until the polenta thickens and slow bubbles "erupt", about 5 minutes. Remove from the heat.
Stir in the Parmigiano and butter. Keep warm until serving.