1Peel potatoes, cut into eighths, and place immediately into a large pot. Add water to cover the potatoes by at least 2 inches and salt well (the water should taste like seawater).
2Bring potatoes to a boil over high heat. Once boiling, reduce heat to medium low and simmer, uncovered, until potatoes are completely tender and just beginning to fall apart, about 20 minutes.
3Drain potatoes in a large colander and let them dry undisturbed for about 5 minutes. Meanwhile, heat broth and butter over medium heat in the pot used to cook the potatoes until mixture is hot and butter is melted. Remove from heat and season with freshly ground black pepper and, if necessary, salt.
4Pass cooked potatoes through a potato ricer into the broth mixture. Fold together, being careful not to overwork the potatoes, until evenly combined and smooth. Taste potatoes, and, if necessary, adjust seasoning.