In a medium saucepan, combine the whole milk and heavy cream over medium heat. Stir frequently and heat until it is steaming, but do not let it boil.
In a separate bowl, whisk the egg yolks and granulated sugar together until the mixture is pale and creamy.
Slowly pour about 1 cup of the warm milk mixture into the egg yolk mixture while whisking constantly to temper the eggs. This will prevent them from scrambling.
Pour the tempered egg mixture back into the saucepan with the remaining warm milk and cream. Continue to stir over medium heat until the mixture thickens slightly, about 5-7 minutes.
Remove from heat and stir in the vanilla extract, ground cinnamon, ground nutmeg, cayenne pepper, and maple syrup until well combined.
Transfer the eggnog to a bowl or pitcher and let it cool to room temperature, then refrigerate until chilled, at least 2 hours or up to overnight.
Serve the eggnog cold, topped with whipped cream, and garnish with cinnamon sticks for a festive touch.
Notes
Adjust the cayenne pepper to your desired spice level.