Cut the melon into bite-sized chunks and freeze them, leaving a few chunks at room temperature for making the liquid base.
Blend the room temperature honeydew melon chunks with the liquid ingredients + mint leaves, until you get a liquid mixture, then add the frozen honeydew chunks. This will give this honeydew smoothie a slush consistency.
Pour about 1 cup of honeydew smoothie in each glass; stir gently. Garnish with mint leaves, if desired.
This honeydew smoothie / slush can be made 1-2 hours ahead. Store in blender jar in freezer, then re-blend on high speed to combine.