Divide mint leaves into two glasses and top with 2-3 thin slices of cucumber per glass. Add 1 oz simple syrup per glass, then muddle until scent and oils of mint have been released.
Top muddled mint and cucumber with 1 1/2 oz gin per glass. Fill glass with ice, then top with sparkling water. Garnish with additional cucumber slices, kumquat slices, and mint before serving.