In a large bowl, mix egg yolks and sugar until you get a creamy consistency. Set aside.
Heat a saucepan on medium heat. Add whole milk, heavy cream, nutmeg, cinnamon, vanilla extract, peppermint extract, and salt
Right when the milk mixture starts to simmer, remove it from the heat.
Using a ladel, add one ladel-full of the milk mixture to the egg mixture while whisking quickly. Keep adding the milk mixture spoonful by spoonful, whisking constantly, until it has all been added to the egg mixture.
Add the nog mixture back into the saucepan on medium heat. Whisk constantly until the mixture slightly thickens, or reaches 160F (71C). Remove from heat.
Pour the nog through a fine mesh strainer into a container. Let the mixture cool, then seal with a lid or plastic wrap and transfer to the fridge. The custard will be ready and fully thickened in about 4 hours.
Remove the peppermint eggnog from the fridge, pour, and enjoy!