Passing the cooked potatoes through a ricer, instead of mashing or processing them, results in an airy, delicate puree. Choose Yukon Gold potatoes for best results; they are the perfect mix of waxy and starchy for a fluffy and creamy mash.
Combine potatoes and salt in a large pot; add cold water to cover by 2 inches. Bring to a boil over high. Reduce heat to medium; simmer, undisturbed, until potatoes are very tender but not yet falling apart, about 20 minutes. Drain; let potatoes stand at room temperature until they look dry, about 5 minutes.
Meanwhile, heat milk and butter pieces in a small saucepan over medium, stirring occasionally, until milk is steaming and butter is melted, about 3 minutes. Remove from heat.
Pass potatoes through a ricer into large pot. Whisk in milk mixture, cheese, and nutmeg. Season with additional salt and nutmeg to taste.