1) Peel and seed the cucumbers and cut into large chunks. Save a few slices for garnish.
2) Put cucumbers, basil and ice in a blender.
3) Blend until slushy, pour the honey through the hole in the top to emulsify it into the slush.
4) Stir in rum, if desired, then pour in a chilled glass.
5) Garnish with a slice of cucumber and a sprig of basil. Serve immediately.
Yields 4 cups