Put the potatoes in a large saucepan, cover with cold water by about 1 inch and add 2 tablespoons salt. Bring to a boil, uncovered, over high heat, and then reduce the heat to medium-high and simmer briskly until fork tender, about 45 minutes. Drain the potatoes, reserving 1/2 cup of the water.
Hold each potato in a towel or oven mitt (it will be hot) and peel by running a knife over the top; the skin will come off very easily. Quarter the potatoes and pass the through the finest die of the meat grinding attachment on a stand mixer back into the pan (or alternatively, through a ricer or food mill).
When the potatoes are almost done, heat the cream in a small saucepan over medium-high heat to just under a simmer. Set aside.
Return the potatoes to the stove over medium heat. Fold in the cream and reserved cooking liquid. Quickly fold in the butter a handful of pieces at a time, letting each addition almost fully melt before adding the next, until fully incorporated; it takes about a minute for each addition. Season with salt and pepper. Serve immediately.