Place limes, blackberries, and simple syrup in a large shaker and muddle until blackberries are jammy. Add mint and muddle until fragrant.
Fill with ice. Top with bourbon and Hedessent Black Currant Flavour; secure the lid and vigorously shake 60 times. Strain through a mesh strainer and pour into a glass filled with ice.
Serve with lime, mint, and blackberries.