Active time: 20 minutes
Total time: 1 hour 20 minutes
In a pitcher, combine eggnog, hazelnut liqueur, and vodka. Refrigerate until chilled, about 1 hour. In a cocktail shaker filled with ice, pour ½ cup of mixture, plus nutmeg to taste, and shake until ice-cold, about 20 seconds. Strain into a martini glass, grate nutmeg on top, and serve. Repeat with remaining mixture and ice.