Put the potatoes in a large saucepan and cover with cold water by at least an inch. Add a generous 1/2 teaspoon salt and bring to a boil. Lower the heat to maintain a steady simmer, cover the pot partially, and cook until the potatoes are quite tender when tested with a metal skewer, 15 to 20 minutes.
Drain the potatoes -- reserving some of the cooking water -- and dump them back in the pot. Dry the potatoes over medium heat, shaking the pan and stirring, until most of the moisture has steamed off. Reduce the heat to very low.
Use the side of a big metal spoon to cut through the skins and flesh of the potatoes, reducing the chunks to a very coarse mash. Stir in the butter and then the Boursin. If you want, loosen the mash with cooking water: Depending on the potatoes, you might need a few tablespoons cooking water or as much as 1/2 cup. Don’t beat vigorously or the potatoes may turn gummy. Stir in the scallions, add salt and pepper to taste, and serve right away.