Cover the potatoes with water in a medium saucepan, bring to a boil over high heat, then reduce the heat to medium-low; simmer until the potatoes are cooked through, about 8-10 minutes. Transfer 1 cup of the potato water to a bowl then drain the potatoes and return them to the hot saucepan. Over low heat, cook the potatoes while shaking to remove the surface moisture, about 1 minute.