At least 15 minutes before starting the eggnog, chill a medium bowl and beaters
from a hand-held electric mixer in the refrigerator or freezer.
In a 2 1/2-quart bowl, combine eggs and sugar. Beat at low speed until mixed.
Gradually increase mixer speed; beat at high speed (highest speed for a hand-held
mixer) for 5 full minutes. Mixture will increase in volume and become very pale;
you'll be able to see definite marks from the beaters in the egg mixture.
All at once, add milk, white chocolate liqueur and rum. Beat on lowest speed
just until mixed; the egg mixture will thin out dramatically.
In chilled medium bowl, beat heavy cream at high speed just to stiff peaks. Scrape
into thinned egg mixture. With large rubber spatula, fold the two mixtures together,
pouring gently from one bowl to another once or twice to aid with blending process.
Serve immediately or chill, covered, for up to 6 hours. If mixture stands for
any length of time in refrigerator, a thinner layer will separate out on the bottom.
Just before serving, fold the eggnog over on itself until thinner layer at bottom
Serve eggnog cold. Garnish each serving with a pinch of finely grated
semisweet chocolate, if desired.