Peel the potatoes and cut them into 1-inch chunks. steam the potatoes, covered, until very tender, about 20 minutes. Press the potatoes through a ricer or the medium disk of a food mill set over a bowl.
In a large nonreactive saucepan, melt 4 tablespoons of the butter. Add the onion and cook over moderately low heat, stirring, until softened. Add the anchovies and stir until melted. Stir in the milk and heavy cream, season with salt and pepper and bring to a simmer. Add the potatoes and stir until smooth and warmed through. Stir in the scallion greens and remaining 2 tablespoons butter and serve hot.
The potatoes can stand at room temperature for up to 4 hours.