In a large saucepan, combine the potatoes, 6 cups water and 1 teaspoon salt. Bring to a boil over high, then reduce to medium-high and cook at a low boil, uncovered, until a skewer inserted into the potatoes meets no resistance, 15 to 18 minutes. Reserve about 1 cup of the cooking water, then drain the potatoes in a colander. Shake the colander to remove as much moisture as possible, then return the potatoes to the pan. Set over low and cook for about 1 minute, occasionally shaking the pan, to evaporate any residual moisture.