In a small saucepan, bring the water, sugar, herbs, and lime peel to a boil. Remove from heat. Cover with a lid and let steep for 10 minutes. Strain and chill in the refrigerator.
For the cucumber juice:
In a small food processor, puree the cucumber. Strain well. You should have about 1/2 cup (180g) juice.
To make a spritz:
In a shaker, combine the vodka, cucumber juice, lime juice, and herb simple syrup. Pour into a rocks or wine glass filled with ice. Top with sparkling water. Garnish with a lime round and herb sprig.