Put honeycrisp apple slices and water in a blender and blend until smooth for homemade apple puree.
Push puree mixture through a fine mesh sieve into a bowl or mason jar to get out as much juice as possible, leaving solids behind.
On a small plate, combine granulated sugar and cinnamon. Brush rims of cocktail glasses (coup glasses work well) lightly with holiday spiced simple syrup and twirl the glasses in the sugar/cinnamon mixture to coat rims.
Pour 4 oz. homemade apple puree, 3 oz. bourbon, and 1 oz. holiday spiced simple syrup into a shaker filled with ice and shake well. Pour into two glasses. Repeat with two remaining glasses.
Garnish each cocktail with apple chips and star anise, if desired.