Put the potatoes into a large pot and add water to come halfway up the potatoes. Cover the pot and bring it to a boil over high heat. When the water begins to boil, carefully drain off about half of it. Return the pot to the heat, cover it again, reduce the heat to low, and let the potatoes steam for about 30 to 40 minutes. Inset a knife to test if done. Turn off the heat and let them sit for 5 more minutes.
Meanwhile, bring the milk to a simmer in a small saucepan, then add the scallions and simmer for 10 to 15 minutes or until soft. Strain the milk, reserving the scallions and the milk separately.
Drain and carefully peel the potatoes and return them to the pot and mash them well. Stir in the scallions and butter, then drizzle in the milk, continuing to mash until they are fluffy. Season with salt and pepper.