Cook the potatoes in a medium saucepan of boiling salted water until tender, about 15 minutes. Drain the potatoes and return them to the pan. Set the pan over moderately high heat and shake for about 1 minute to dry out the potatoes. Using a potato masher, mash the potatoes in the pan. Stir in the cream, Parmigiano-Reggiano and the 3 tablespoons of butter and season generously with salt and pepper. Scrape the mashed potatoes into a large bowl and set aside to cool to room temperature.