Pour the cooled coffee, chocolate syrup, vanilla extract, molasses, and ground ginger into a cocktail shaker or lidded jar. Secure the lid and shake until everything is fully blended and the mixture looks smooth and glossy.
Add a generous handful of ice cubes to the shaker, then shake again for another 10–15 seconds to thoroughly chill the mixture.
Strain the chocolate-coffee mixture evenly into 4 small glasses or festive mugs.
Gently top each glass with the heavy cream or whole milk, letting it float and swirl through the drink for a layered effect.
Finish with a cloud of whipped cream, then decorate with crushed candy canes and gingerbread cookies, if desired. Serve immediately and enjoy this cozy North Pole Cocktail mocktail while it’s cold and creamy.