Place potatoes in a bowl and wash under cold, running water until water runs clear. Place in a medium saucepan with salt. Add enough water to generously cover. Bring to a boil, reduce to a simmer, and cook, uncovered, until soft, about 15 minutes.
Meanwhile, place the peas and scallions in a small saucepan over medium heat, cover with the milk and add the sugar. Slowly bring to a boil, reduce the heat and simmer for 3 to 4 minutes, or until peas are tender. Turn off the heat and let the milk sit.
Peel and mash the boiled potatoes, using a fork or food mill, and while potatoes are hot, add the warm milk mixture. Beat in some of the butter, and season to taste with salt and pepper. Serve with remaining butter melting on top.
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