Softened vanilla ice cream gives this drink the lusciousness you want in a holiday cocktail. You could also use heavy cream in its place, but I really like the texture of the soft vanilla ice cream.
Vanilla vodka would also work well in this cocktail.
You do not specifically have to use Bailey's Irish cream - any Irish Cream liqueur will work well.
I'm using my homemade gingerbread syrup, but you can also use storebought gingerbread syrup. The common ones you find are for flavoring coffee.