Place the potatoes in a colander and rinse under running water, tossing with your hands, for 30 seconds.
Transfer the potatoes to a Dutch oven, add water to cover by 1 inch, and bring to a boil over high heat.
Decrease heat to medium and boil until potatoes are tender, 20-25 minutes.
Meanwhile, heat the butter and cream in a small saucepan over medium heat until the butter is melted, about 5 minutes; keep warm.
Drain the potatoes and return them to the Dutch oven; stir over low heat until the potatoes are thoroughly dried, 1-2 minutes.
Set a ricer or food mill over a big bowl and press or mill the potatoes into the bowl; gently fold in the warm cream mixture and salt with a rubber spatula until the cream is absorbed and the potatoes are thick and creamy.