In a small saucepan, combine equal parts granulated sugar and water over medium heat. Stir until the sugar completely dissolves, then bring the mixture to a gentle boil. Once boiling, add a cinnamon stick and reduce heat to low. Let it steep for at least 30 minutes or cool completely and sit for up to 3 hours.

While the simple syrup is infusing, wash a fresh, ripe peach thoroughly. Remove the pit and slice it into smaller chunks. Place the peach pieces in a blender and puree until smooth.

In a chilled copper mug, add 2 oz of your freshly made peach puree. Pour in 1.5 oz of vodka, along with 3 oz of spicy ginger beer, and 0.5 oz of lime juice, followed by 0.5 oz of the cinnamon simple syrup.

Stir gently to combine. Check the mixture for flavor balance and adjust sweetness if desired. Add ice cubes to the mug.

Garnish the cocktail with slices of fresh peach or a sprig of mint. Serve immediately and enjoy.