In a Collins glass, layer ice and three cucumber slices. Grab a shaker and muddle the rest of the cucumber slices and one sprig of Basil. Add the rest of the ingredients (except soda), fill with ice and give this a vigorous shake. Strain over prepped glass and top with soda. Garnish with basil sprig.
To add a bit of complexity to this, you can use Orgeat Syrup (aka almond syrup) that would pair beautifully with this bright, refreshing cocktail.