Put the potatoes and scallions in a large saucepan and add enough water to cover by 1 inch. Add the salt, cover and bring to a boil. Reduce the heat and simmer the potatoes until tender when pierced, about 25 minutes.
Drain the potatoes, reserving 1 cup of the cooking water. Return the potatoes to the saucepan and coarsely mash them by hand. Add the mascarpone and parsley; add a little of the cooking water if the potatoes are too stiff. Season with salt and white pepper and serve at once.
Using small unpeeled boiling potatoes saves a great deal of time; the skins of Yukon Golds are particularly tender. If you don't like the skins, use larger baking potatoes and peel and quarter them.