Peel the potatoes and slice as thinly as possible on a mandoline directly into a large, 8-quart container filled with 4 quarts of cold water. Cover and refrigerate overnight.
Drain the potatoes and rinse with clean, cold water; spin dry in a salad spinner. Transfer the potatoes to an 11-quart pot, cover with the milk and set over medium heat. Bring to a simmer, about 35 minutes. Reduce the heat in order to maintain a simmer and cook, uncovered, until the potatoes are fork tender and beginning to fall apart, 25 to 30 minutes.
Reserve 1 cup of the cooking milk. Drain the potatoes thoroughly in a colander and return them to the pot. Press the potatoes through a ricer into a large mixing bowl. Add the reserved hot milk, butter and salt and use an electric hand mixer to whip on low speed for 15 to 30 seconds. Do not overwhip.