In a medium bowl, whisk together the eggs and sugar until the mixture is smooth and lighter in color.

In a saucepan, combine the milk, heavy cream, vanilla extract, ground nutmeg, and ground cinnamon. Heat over medium heat, stirring gently until it begins to simmer.

Slowly pour the heated milk mixture into the egg-sugar mixture, whisking constantly to prevent the eggs from scrambling.

Return the combined mixture back to the saucepan and heat over low heat, stirring continuously for about 5-7 minutes until thickened.

Remove from heat, pour the eggnog into a large bowl or pitcher, and allow to cool.

Once cooled, cover and refrigerate for at least two hours to let flavors meld.

Serve in chilled glasses, garnished with extra nutmeg or cinnamon if desired.