Peel the potatoes and cut them in 1½ to 2-inch chunks. Place the potatoes in a large saucepan, add water to cover by one inch, and add 2 tablespoons salt. Cover, bring to a boil, lower the heat, and simmer uncovered for 15 minutes, until the potatoes are very tender when pierced with a small paring knife. Drain and set aside.
Meanwhile, cut the butter in ½-inch dice and put it back in the refrigerator.
After the potatoes are drained, pour the milk into a small saucepan set over low heat and heat the milk just until it simmers. Turn off the heat.
Place a food mill fitted with the finest blade on top of the large saucepan. Process the potatoes into the pan. With the heat on low, vigorously whisk in the cold butter several bits at a time, waiting for each addition to be incorporated before adding more butter. When all the butter is added, slowly whisk in enough of the hot milk to make the potatoes the desired consistency—creamy but still thick. Add 2 teaspoons salt and 1 teaspoon pepper. Whisk in the lemon zest, sprinkle with salt, taste for seasonings, and serve hot.
Lemon gets bitter as it sits so these potatoes are best served the day they’re made. Prepare them completely without the zest and set them aside at room temperature. Reheat in a bowl set over a pan of simmering water, adding warm milk, as needed, until the texture is right. Whisk in the lemon zest just before serving.
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