How to Make It
Preheat oven to 375°F. Grease an 8-inch square baking dish with the butter; sprinkle the bottom and sides with the Parmesan. Set aside.
Place the potatoes in a large pot with salted water to cover and bring to a boil over high. Reduce heat to medium- low and simmer until tender, about 12 minutes. Drain and place in a large bowl with the milk. Mash with a potato masher until almost smooth; cool 10 minutes. Whisk in the cream, Cheddar, egg yolks, chives, salt, and pepper.
Place the egg whites in the bowl of an electric mixer fitted with a whisk attachment. Beat on medium until the whites are glossy and stiff, 4 to 5 minutes. Stir a third of the beaten whites into the potato mixture. Fold in the remaining whites just until incorporated. Transfer to the prepared baking dish and bake until golden brown and puffy, about 30 minutes.