Roughly dice the honeydew melon and cucumber. If the skin of the cucumber is tough, peel it before chopping.
Add all of the ingredients to the blender and blend until smooth.
Transfer to a container and refrigerate for at least 20 minutes, but up to overnight before serving.
Optionally, garnish with additional mint leaves and thinly sliced cucumber.
Notes
Sugar and crushed red pepper flakes are optional in this soup. If your melon isn't very ripe, add in the sugar. If you like a kick of heat, add in the crushed red pepper flakes. Swirl in some sour cream or plain Greek yogurt if desired. Or topped with shredded prosciutto.