Begin by muddling the blueberries, basil leaves and simple syrup in a cocktail shaker. Gently crush the blueberries to release their juices and let the aroma of basil infuse the mixture.
Add ice, gin and freshly squeezed lime juice to the shaker.
Shake vigorously for about 15-20 seconds to ensure the flavors are thoroughly combined and infused.
Strain the mixture into a glass filled with ice cubes.