This hearty side is made with new potatoes, which -- since they are harvested early and picked before their sugars have converted to starch -- are crisp, waxy and high in moisture.
In a 5-quart saucepan, cover potatoes with salted water. Bring to a boil; reduce to a simmer. Cook until tender when pierced with the tip of a paring knife, 20 to 25 minutes. Drain; return to pan. Cook over medium-high, stirring, until dry, 1 to 2 minutes.
In a small saucepan, bring milk to a simmer. Mash potatoes with butter, horseradish, hot milk, and 1 teaspoon salt.
If too thin, cook over medium heat, stirring, until thickened.