Boil potatoes in well-salted water until tender, about 15 minutes. Drain well in a colander and place in the bowl of a stand mixer with a wire whisk attachment. Beat at medium speed for 2 to 3 minutes to allow steam to escape. Turn off mixer and add cheese, baking powder, salt, pepper, cayenne and nutmeg. Beat again for a minute or so. Add butter and cream, mixing slowly, then increase speed to medium and drizzle in beaten eggs. Stop and scrape down bowl with rubber spatula to make sure ingredients are incorporated evenly. Beat at medium-high speed until mixture is smooth, 2 to 3 minutes. Serve immediately in a heated bowl. Alternatively, transfer potatoes to a 2-quart baking dish, cover with foil and let stand at room temperature. Reheat for 30 to 40 minutes at 350 degrees, until piping hot. (If you want the top browned, remove foil halfway through baking. Otherwise, give the potatoes a stir before serving.)