Add the gin, lime juice, and simple syrup to a cocktail shaker.

Add cucumber slices to the shaker and muddle them vigorously to release their flavor.

Add mint leaves to the shaker and gently press them with the muddler to release their aromatic oils without shredding them.

Fill the shaker with ice and shake vigorously for about 10-12 seconds.

Double strain the mixture into a chilled cocktail glass.

Garnish with a cucumber slice or a sprig of mint.