In a large bowl or the bowl of a 4 quart (See Recipe Notes) slow cooker, place the egg yolks and granulated sugar, and whisk vigorously until smooth. Add the milk and then the cream and optional rum in a slow but steady stream, whisking constantly until well-combined. Add the cinnamon stick and whole nutmeg seeds. The mixture should be smooth and relatively thin.
If you’ve used a large bowl, transfer the mixture to the bowl of a 4-quart* slow cooker. Cover the slow cooker, turn it on low and set for 2 hours. Cook for 1 1/2 to 2 hours, whisking a few times if you think of it, until the mixture is thick enough to coat the back of a spoon. Do not overcook or the mixture will clump and curdle.
Remove and discard the whole nutmeg and cinnamon. Unplug the slow cooker and allow the eggnog to cool for at least an hour before transferring to covered container and refrigerating until chilled. If you think that the milk has clumped or curdled at all, run the eggnog through a fine mesh sieve before chilling. Serve cold or warm with a sprinkle of grated fresh nutmeg.
Notes
If you only have a 6-quart slow cooker, use that but you will need to whisk more often and monitor more closely to ensure that the eggnog doesn’t curdle.