In a cocktail shaker or sturdy glass, add the cucumber slices and mint leaves.
Gently muddle the cucumber and mint together for about 30 seconds, pressing down to release the oils and juices without tearing the mint leaves completely.
Add the lime juice, simple syrup, and rum if using, then fill the shaker with ice and shake vigorously for 15 seconds.
Strain the mixture evenly into two glasses filled with fresh ice.
Top each glass with sparkling water and stir gently to combine.
Garnish with lime wedges, cucumber ribbons, and extra mint sprigs before serving immediately.