Smoothly blend milk with cornstarch and 0.125 tsp nutmeg in a 1 1.5 qt pan, set aside. With a mixer, whip whites until foamy. Beating at high speed, gradually add sugar until whites hold short peaks. Stir milk mixture over high heat until just boiling. With mixer on medium speed at once pour hot milk into whites, scraping down bowl sides. Let stand at least 4 minutes. Add rum to eggnog, serve hot or cover and chill until cold, about 3 hours or up to 8.

Pour mixture through a fine strainer in glasses. Dust with nutmeg.