In a large saucepan, heat 4 cups milk until very hot.
In a medium bowl, beat yolks from 4 large eggs with an electric mixer on medium-high speed until pale and thick, about 4 minutes. Add 1 1/4 cups confectioners' sugar and beat until stiff, about 1 minute. Beat in 1 1/2 tsp. vanilla extract.
In a clean medium bowl with clean, dry beaters, beat 4 large egg whites at medium-high speed until whites form stiff peaks when beaters are lifted. With a rubber spatula, fold egg whites gently into yolk mixture. Place 3 Tbsp. egg mixture in each of 8 cups. Add 2 Tbsp. rum and 1/2 cup hot milk to each. Stir until just blended. Top each with a pinch of nutmeg and serve hot. Serves 8.
Note: To reduce the risk of food-borne illness, people with health problems, the very young, the elderly and pregnant women may wish to avoid raw eggs.