Add ice and remaining ingredients to shaker, shake vigorously to combine well.
Strain into a cocktail glass over ice. Garnish with cucumber slices.
To make simple syrup, combine one part water with one part white granulated sugar in a small saucepan. Heat over medium heat, whisking until sugar is dissolved. Do not boil. Remove from heat, allow to cool. Simple syrup can be kept in a sealed container in the refrigerator for up to one month.