Step 1

Combine the syrup and condensed milk in a cocktail shaker. Fill with ice, seal the shaker, and shake for 10 to 15 seconds, until well chilled. Double-strain into a collins glass filled with fresh ice, then top with the Coca-Cola. Gently stir with a barspoon to incorporate. To serve, float the star anise on the foam, if using.

Step 2

In a small saucepan, combine 3⁄4 cup water with the cinnamon over medium heat and bring to a boil. Whisk in the sugar, coffee, and vanilla; turn the heat down to low; and gently simmer for 5 minutes. Add the star anise, stir the mixture once, and remove from the heat. Let cool to room temperature, about 45 minutes. Then fine-strain the mixture, pressing on the solids to extract as much liquid as possible, and discard the solids. Store the syrup in an airtight container in the refrigerator for up to 2 weeks.