Begin by preparing the cucumber. Wash it thoroughly and cut off both ends. If desired, you can peel the cucumber, but it's not necessary. Slice the cucumber into thin rounds or dice it, depending on your preference. Set aside a few slices for garnish.

In a cocktail shaker, add the remaining cucumber slices and muddle them gently using a muddler or the back of a spoon. Muddling helps release the flavors and aromas of the cucumber.

To the cocktail shaker, add the vodka, fresh lime juice, and simple syrup.

Fill the cocktail shaker with ice cubes, ensuring it's about three-quarters full. Close the shaker tightly.

Shake the mixture vigorously for about 15 seconds, allowing the ingredients to combine well and chill.

Prepare a serving glass by filling it with ice cubes. Strain the cocktail mixture from the shaker into the glass, discarding any cucumber pulp.

Top off the glass with soda water to your desired level of carbonation.

Stir gently to combine all the ingredients.

Garnish your cucumber vodka cocktail with fresh mint leaves and a slice of cucumber.

Serve and enjoy!