Place the potatoes in a colander; rinse briefly under cool water while tossing. Drain well, then transfer to a large (7- to 8-quart) Dutch oven; distribute evenly. Add 1½ cups water; the potatoes will not be fully submerged. Sprinkle with 1½ teaspoons salt, then drop in the chunks of butter.
Bring to a boil over medium-high, then cover, reduce to medium-low and simmer, stirring occasionally, until the potatoes fall apart when poked with a fork, 25 to 30 minutes. Uncover and cook over medium, stirring only once or twice, until only a little starchy liquid remains in the bottom of the pot, 3 to 5 minutes. Off heat, use a potato masher to mash the potatoes until smooth.
If serving right away, add ½ cup boiling water and mash until the water is incorporated. Taste and season with salt and pepper. Transfer to a warmed serving dish and sprinkle with chives and additional pepper.
If making ahead, transfer to a container and cool completely, then cover tightly and refrigerate up to 2 days. To reheat, transfer the potatoes to a large saucepan and add ¾ cup water. Cover and cook over medium-low, mashing occasionally (do not stir), until the potatoes are warm and fluffy, about 20 minutes; add more water a few tablespoons at a time as needed to adjust consistency. Taste and season with salt and pepper. Transfer to a warmed serving dish and sprinkle with chives and additional pepper.
