In a large glass or double old fashioned glass, muddle basil leaves, blackberries, and coarse sugar using a wooden spoon or muddler until berries release their juices. Top with ice and set aside.
In a cocktail shaker, fill with ice, lemon juice, simple syrup, and Black Currant flavour and shake hard 60 times.
Strain into the prepared glass and top with club soda. Stir with a tall spoon; garnish with lemon slices and blackberries.