In a large pot, bring 2 quarts of water and 1 tablespoon of salt to a boil. Meanwhile, peel the potatoes and cut them into 1 1/2-inch cubes. Add them to the boiling water and bring the water back to a boil. Lower the heat and simmer uncovered for 10 to 15 minutes, until the potatoes fall apart easily when pierced with a fork.
Meanwhile, heat the milk and butter in a small saucepan, making sure it doesn't boil. Set aside until the potatoes are done.
As soon as the potatoes are tender, drain them in a colander. Place a food mill fitted with a small disk/blade over a heatproof bowl. Pass the potatoes through the food mill, turning the handle back and forth. As soon as the potatoes are mashed, stir in the hot milk mixture with a whisk or rubber spatula. Add enough buttermilk to make the potatoes creamy. Add 1 teaspoon of salt and the pepper, and serve hot. To keep the potatoes warm, place the bowl over a pan of simmering water for up to 30 minutes. You can add a little extra hot milk to keep them creamy.