Preheat your grill to high heat. Place the peach halves and the lemon half onto the grill and cook undisturbed until charred grill marks appear and the fruits have softened.
Transfer the peaches and lemon to a cutting board to cool then dice up the peaches and add them, along with any juices, to large mason jar or a cocktail shaker. Add in the juice of the grilled lemon, the mint, sugar, and simple syrup and, using a wooden spoon or a cocktail muddler, mash everything together until the peaches have broken down and are saucy.
Add in the bourbon and ice and shake vigorously until well chilled. Strain the cocktail into two glasses and top with the soda water or ginger ale. Garnish with fresh mint and a slice of peach.
In a small saucepan, combine the sugar and water and bring it to a simmer over medium heat. Allow the mixture to simmer until the sugar is fully dissolved, about five minutes. Remove from the heat and allow to cool fully before transferring to a container to be stored in the fridge for up to one month.
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