Separate the eggs very carefully, making sure no yolk gets into the whites. Refrigerate the whites in a covered container.
In a pan off the fire, whisk the egg yolks with the sugar until it becomes pale yellow and thicker. Add the nutmeg, vanilla, cream, and one cup of the half-and-half. Whisk until blended.
Heat the pan over a very low fire while stirring, with a meat thermometer in the mix. Watch for a temperature reading of 175. Don't overheat or cook longer than needed to reach this temperature.
Remove from the heat, and add the remaining half-and-half. Use a fine sieve to strain the mixture into the container you'll use to refrigerate it, and put it into the refrigerator.
When you're ready to serve the egg nog, beat the egg whites with the cream of tartar until it makes soft peaks. With a rubber spatula or wooden spoon, stir the beaten egg whites into the refrigerated egg nog until most (but not all) of the streaks are blended in.
If you'd like to add something interesting (i.e. brandy, Bourbon, or dark rum), a half-cup of the liquor is about right. Serve with some more nutmeg (freshly grated, if possible) over the top.
