First make the peach simple syrup by combining the sugar, water and peach in a small saucepan. Muddle the peach into the sugar water and heat on medium until the syrup begins to simmer. Allow to cook for 5 minutes. Then remove from heat and allow to cool. Store syrup in refrigerator until ready to use.
To make the cocktail, combine the rye, chilled peach syrup, and bitters in a mixing glass with ice. Stir ingredients well and then strain into a rocks glass and add ice. Top off with a splash of club soda if you please. Garnish with a mint sprig.
Recipe by Oakhurst Kitchen at http://oakhurstkitchen.com/peach-mint-old-fashioned-cocktail/