To a small saucepan, add granulated sugar, brown sugar, ground cinnamon, ground ginger, ground cloves, molasses, vanilla extract, and ½ cup water. Stir together over medium-high heat and bring to a boil.
Once ingredients begin to boil, reduce heat and allow to simmer, stirring constantly, for about 3 minutes.
Remove from heat. Immediately transfer to a sealable heat-proof container and place in the refrigerator to cool while preparing the espresso in the next step.
In a small bowl or cup, add instant espresso granules and 1 tablespoon water. Stir well until all granules have dissolved.
Remove syrup from the refrigerator and stir-in the espresso mixture. Place syrup back into the refrigerator to cool for at least 30 minutes.
Make the Cocktail
Run an orange wedge around the rim of your cocktail glass. Tilting the glass at a 45-degree angle, dip the dampened rim into a shallow plate of crumbled gingerbread cookies. Rotate the glass, continuing to dip its edge into the crumbs until the rim is well coated.
Fill a cocktail shaker ½ full of ice. Add milk, gingerbread espresso syrup, black spiced rum, and coffee liqueur to the shaker. Secure the lid and shake until chilled throughout (about 20 seconds).
Pour into prepared cocktail glass. Top with whipped cream, a sprinkle of crumbled gingerbread cookies and a cinnamon stick, if liked.
Notes
Chill syrup first: A cooled syrup blends better into the cocktail. Use fresh spices: The flavor is stronger and more aromatic. Shake well: A vigorous shake ensures the drink is creamy and smooth. Prep rim ahead: Coat glasses with cookie crumbs before mixing to save time.