Set the sous vide to 144°F (62°C).
Combine eggs, sugar, whole milk, heavy cream, vanilla extract, nutmeg in a blender.
Puree until smooth, frothy, and the sugar has dissolved... about 30 seconds.
Transfer to a large zip top bag, add the cinnamon stick and seal using the water immersion technique.
Leave the zip top bag open so as the eggnog bubbles pop, the can escape.
Set the timer for 1 hour. Massage the bags several times throughout the cooking process.
When the timer goes off, remove the bag from the sous vide water bath and cool completely in an ice bath.
Remove the cinnamon stick.
Add the rum and brandy to the eggnog.
10. Serve immediately or refrigerate for up to three days. Add additional bourbon and brandy if desired.