Fill 4 cocktail glasses evenly with the cucumber, mint, and kumquats. Add 1 teaspoon of superfine sugar to each glass. Using a muddler, smash the ingredients in each glass slightly to release flavors and juices.
Add 1 TBS lime juice into each glass.
Add crushed ice into each glass filling 3/4 full. Add the vodka, orange liquer, and club soda in order to each glass.