Combine water and sugar in a small saucepan and bring to a boil. Remove from heat, add the cinnamon stick, and cover.
Let it steep for 30 minutes up to 3 hours, depending on desired cinnamon intensity.
Strain the syrup into a clean jar and refrigerate until ready to use.
Prepare the Peach Moscow Mule:
Blend fresh peach until smooth to make the puree. If fresh peaches aren’t available, use peach nectar or thawed frozen peaches.
In a copper mug or glass, combine the peach puree, ginger beer, vodka, lime juice, and cinnamon simple syrup.
Stir well to combine.
Add ice and serve immediately.
Notes
A refreshing summer cocktail with sweet peach, zesty lime, and warming cinnamon. Perfect for individual servings or scaled up into a pitcher for entertaining. Frozen peach slices can be used as ice to avoid dilution.