***If using store-bought eggnog, skip to step 7***
In a large saucepan, combine milk, cream, cinnamon, vanilla, and nutmeg.
Bring to the boil over a medium heat. Be careful when bringing to a boil that the milk doesn't boil over the pan. As soon as you see it bubbling, remove from heat.
Allow to sit for at least 5-10 minutes to steep. (you want to make sure the milk mixture isn't hot enough to cook the eggs once added. So allow to sit for a little bit off the heat before the next step) :)
In a large stand mixer, beat eggs and sugar on medium high/high until fully combined.
Pour egg mixture into the milk and whisk quickly until fully combined.
Add the bourbon or spiced rum to the eggnog and stir to combine.
Refrigerate at least 2 hours or until cold (if mixture is already cold you can skip this step)
Add the eggnog to your ice cream maker and prepare according to manufacturers instructions. When the ice cream is almost complete, add in the peppermint crunch baking chips.
When the ice cream is almost done, you can make your syrup. Bring the sugar, water, and crushed candy canes to a boil in a small saucepan. Reduce to a simmer and allow to cook down for 10 minutes. Pour over the completed ice cream for a special treat!