Combine the gin, lime juice, basil, cucumber and simple syrup in a high-powered blender and blend until completely smooth.

Strain the liquid through a coffee filter or a muslin cloth into a cocktail shaker. This will take about 15 minutes - you can stir it gently to help it along, if needed. Discard the pulp left in the filter/cloth, then add a handful of ice into the shaker, clamp on the lid and shake until it has frosted on the outside.

Meanwhile, use a speed peeler to peel two thin long strips of cucumber. Lay each slice of cucumber around the inside of each of your coupe glasses and gently slice off any excess that protrudes over the side.

Strain the cocktail into your prepared glasses and enjoy immediately.