Add eggnog, vodka, and amaretto to a cocktail shaker. Shake for at least 20 seconds to thoroughly mix.
Prepare your martini glass by dipping the rim in water and then dipping again into a small plate of cinnamon sugar.
Strain martini into prepared glass and garnish with a cinnamon stick and freshly grated nutmeg, if desired.
Notes
If you prefer an extra chilled drink, you can either strain the cocktail into a pre-chilled glass or add a few ice cubes into the cocktail shaker before mixing!