To make the mint-infused bourbon, pour 300ml out of the bourbon bottle (keep this in another bottle and enjoy whenever), then top the bottle up with the sugar syrup and stuff as much mint as you can into the bottle. Leave in a warm place for a few hours but preferably overnight.
To make the cocktail, put the peach in the bottom of a glass, add the bitters and muddle. Add the minted bourbon, fill the glass with crushed ice and churn.
Top with more crushed ice and garnish with a sprig of mint.