Bring a large saucepan of water to a boil. Add the whole potatoes and cook over moderate heat until tender, 20 minutes. Drain and wipe out the saucepan. Working with 1 potato at a time, pass the potatoes through a ricer into the saucepan.
In a small saucepan, melt the butter in the milk over moderate heat. Gradually whisk the hot milk into the potatoes and season generously with salt. Cook over moderate heat, whisking, until hot. Serve.