Muddle two of the pieces of cucumber in a cocktail shaker with the simple syrup. Add the rum and lime juice, fill the shaker with ice and shake until chilled. Strain using a fine strainer into a chilled coupe. Garnish with the remaining slice of cucumber.
Using cucumber in a cocktail is a great way to make a refreshing beverage. This cocktail takes the typical daiquiri in a different direction and gives you something complex and drinkable.
Rhum Agricole is made from freshly squeezed sugar cane juice instead of molasses like most other rums. This method gives it a unique grassy flavor that works so well in combination with the cucumber. If you don't have Rhum Agricole on hand and don't want to grab a bottle, any other white rum would work great here too.