Peel and slice the cucumber. Cut the honeydew melon into 1-inch chunks.
Add cucumber slices and melon chunks to the blender. Pulse until smooth.
Strain the mixture through a fine-mesh strainer into a cocktail shaker.
Add vodka, lime juice, and simple syrup to the shaker.
Fill the shaker with ice and shake for 15 seconds.
Strain into a Collins glass filled with fresh ice.
Top with club soda and stir gently.
Garnish with a cucumber ribbon and melon ball.
Notes
The drink stays fresh in the refrigerator for up to 24 hours without the club soda.For a mocktail version, skip the vodka and add extra club soda.Use chilled ingredients for the best results.Make simple syrup by heating equal parts water and sugar until dissolved, then cooling.