Combine the Captain Morgan Original Spiced Rum, apple cider syrup, lime juice, bitters, and 1 piece of star anise in a cocktail shaker and shake vigorously. Strain the liquid into a cocktail glass. Garnish with the other piece of star anise.
In a small saucepot over medium-high heat, cook the apple cider and cinnamon sticks until the cider is reduced to 1 cup, about 10 to 15 minutes. Add the brown sugar and remove the pot from heat. Stir the mixture until the sugar is dissolved. Allow the syrup to cool before use.