Add the heavy cream, ½ teaspoon salt, and ½ teaspoon pepper, and stir to combine. Bring the cream to a simmer over medium-low heat. Cook, frequently stirring, scraping the sides and bottom to make sure the cream does not curdle. Reduce the sauce to about 1 cup. This takes around 8 minutes or so. It should be lightly thickened, coating a spoon. Turn off the heat and stir in the freshly grated Parmesan cheese until fully incorporated. Season with the remaining salt and pepper.