Thinly slice 3 rounds of cucumber.
Pick 4 fresh basil leaves and set a sprig aside for garnish.
Squeeze lime juice until you have 1 oz (about half a lime).
In a cocktail shaker, add cucumber slices and basil leaves.
Gently muddle using a muddler or the back of a spoon to release the flavors.
Pour in 2 oz of gin (or vodka), 1 oz of lime juice, and 0.75 oz of simple syrup.
Fill the shaker with ice until three-quarters full.
Secure the lid and shake vigorously for 15-20 seconds, or until the shaker feels frosty.
Using a fine-mesh strainer, pour the cocktail into a chilled martini glass to remove any cucumber or basil bits.
Top with a fresh basil sprig or a cucumber ribbon for an elegant finish.
Sip and enjoy your perfectly refreshing martini!