Prepare the garnish. Cut an apple in half lengthwise, then cut into thin slices. If you use the slices from the middle of the apple you'll get that pretty star shape from where the seeds were. Put the apple slices into a bowl of ice water with a squeeze of lemon or lime juice. This will keep them from turning brown.
Fill a cocktail shaker with ice. Add apple cider, bourbon, spiced syrup, and bitters and shake with a fury for about 10 seconds. Strain into a short glass and garnish with an apple slice and star anise.
Combine water, sugar, star anise, and cloves in a small saucepan. Bring to a boil over medium heat and cook, stirring occasionally, until the sugar is dissolved. Take off heat and allow to cool. Strain out spices.