Make the simple syrup.
In a medium saucepan combine water, cinnamon sticks, whole cloves and star anise, then set over medium-high heat and bring to a boil.
Reduce the heat to medium, then add in the light brown sugar and stir until the sugar has completely dissolved.
Remove the saucepan from the heat, cover and let cool completely.
Taste the syrup after 1-2 hours and continue to steep until the desired flavor intensity is reached.
Strain out the spices using a fine-mesh sieve and transfer to a container with a tight fitting lid; store in the fridge until ready to use.
Make the apple cider martini.
Optionally, rub the rim of a coupe or martini glass with a lemon slice, then dip the rim in a cinnamon sugar mixture and set aside.
Fill a cocktail shaker halfway with ice, then add in the bourbon, apple cider, spiced simple syrup and lemon juice.
Cover with the cocktail shaker lid and shake vigorously for 15 seconds, then strain directly into the prepared glasses.
Garnish with lemon peel or apple slice and enjoy!