Add peach slices and mint to a tumbler glass. Using a muddler, smash the peaches and leaves together as much as possible. The more they are smashed, the more flavor that emerges from them. Add bourbon and honey and mix together.
Fill two short glasses with ice about 3/4 full. Strain peach mixture over each glass evenly. I had to use a small metal sieve to squeeze all the flavor our of the peaches but prevent the pulp and leaves from going through.
Fill glasses with ginger beer and stir together to combine. Garnish with a mint leave and a thin slice of peach. Serve immediately.