Cut the peeled cucumbers in half and scrape out the seeds. Then, chop them into chunks and place in blender. Add the remaining ingredients (except olive oil) and blend until smooth. Pour the mixture into a serving bowl and stir in the olive oil.
You can save some of the basil for a garnish and this chilled soup pairs nicely with grilled chicken or shrimp for a perfect summer meal. Also can add sliced avocado.