To a small saucepan, add ½ cup water, ½ cup granulated sugar, ½ cup diced fresh peaches, and 1 cinnamon stick.
Heat over MED heat and bring to a simmer, stirring occasionally. Simmer for about 5-7 minutes, until peaches are soft and tender.
Use a spoon or fork to lightly mash the peaches as the syrup is simmering.
Place a mesh sieve over a mixing bowl or a jar, and strain the syrup, pressing gently to get all the peach flavor out of the peaches.
Set bowl or jar aside to cool.
To a cocktail shaker, add ¼ cup fresh peaches, 2 oz cinnamon peach syrup, and 1 oz lemon juice.
Muddle using a cocktail muddler or the handle of a wooden spoon, until they're very juicy.
Add 4 oz bourbon, and fill the shaker about halfway with ice cubes. Add the lid and shake vigorously for about 15 seconds, until very cold.
Add ice to 2 rocks or double old fashioned cocktail glasses, then strain the cocktail into them.
Add any garnishes desired, and serve cold.
