Split the vanilla bean lengthwise and scrape out the seeds. In a saucepan, combine the milk and heavy cream. Add the vanilla bean and seeds. Heat over low heat, being careful not to boil.
In a large bowl, whisk together the egg yolks and sugar until light and creamy.
Slowly drizzle the warm milk mixture into the egg yolk mixture, whisking constantly to prevent the eggs from curdling. Pour the mixture back into the saucepan.
Cook over low heat, stirring constantly, until the mixture thickens slightly, about 8-10 minutes. Do not boil.
Remove from the heat and let cool to room temperature. Stir in the rum and a pinch of nutmeg. Mix well.
Pour the eggnog into a clean bottle and refrigerate for at least 4 hours to allow the flavors to meld. Serve chilled, garnished with a little grated nutmeg.
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