Grease 6- to 8-cup ovenproof baker. Boil potatoes in salted water until tender, 15 minutes. Drain potatoes and mash with cream cheese. Add sour cream, milk, chives, salt, and pepper. Transfer potatoes into prepared dish; dot with chilled butter. Sprinkle with parmesan. (Can be made 2 hours ahead; let stand at room temperature.)
Bake potatoes at 350°F until brown on top, about 35 minutes.