A classic mash gets the Cinderella treatment when it's bolstered by the luxurious addition of walnut oil.
Place potatoes in a large pot, and add enough cold water to cover by 2 inches. Add 1 teaspoon salt. Bring to a boil, and cook until tender, about 10 minutes. Drain, and pass hot potatoes through a ricer or a food mill into a large bowl. Cover to keep warm.
Combine milk, butter, and 1 tablespoon salt in a saucepan over medium heat, and cook until steaming but not bubbling. Add hot-milk mixture to potatoes, and stir until smooth. Stir in oil. Season with pepper.
Just before serving, beat potato mixture with a whisk until fluffy, 3 to 5 minutes. Season with salt to taste.
Puree can be made up to 1 hour ahead; transfer to a heatproof bowl, cover, and set over a pan of barely simmering water.