Muddle the balsamic syrup, basil and sugar cube in a mixing tin. Add bourbon and ice and shake hard. Strain over fresh ice cubes into an Old Fashioned. Top with ginger beer and garnish with basil leaf.
Balsamic Syrup: Combine 1/4 cup balsamic vinegar and 1/4 cup simple syrup (1:1) in a saucepan over medium-high heat. Bring just to a boil, reduce heat to medium-low and let simmer for one minute, stirring occasionally. Remove from heat and let cool completely.