In a large saucepan, whisk together eggs, egg yolk, sugar, vanilla and peppermint extract. Cook over medium heat for 5 minutes. Pour milk into saucepan and whisk into the mixture. Turn up the heat and cook until thick (eggnog will coat the back of a spoon).Remove from heat and let cool (or place in the refrigerator to speed up the process). For candy cane rim place 2 candy canes in a plastic bag and crush using a rolling pin. Place the crushed candy canes into a deep bowl or onto a plate. Rim your glass with honey or Karo syrup and dip your glass into crushed candy canes to rim glass. Pour eggnog into glass and garnish using a whole candy cane. As candy cane seeps into eggnog the eggnog will take on a soft pink hue.

Enjoy!