Peel cucumber to leave alternating green stripes. Slice the cucumber in half lengthwise; scrape the seeds out with a spoon. Using a mandoline or sharp knife, cut into very thin slices. Place in a double layer of paper towel and squeeze gently to remove any excess moisture.
Combine vinegar, sugar and salt in a medium bowl, stirring to dissolve.
Add the cucumbers and sesame seeds; toss well to combine.
Tip: To toast sesame seeds, heat a small dry skillet over low heat. Add sesame seeds and stir constantly until golden and fragrant, about 2 minutes. Transfer to a small bowl and let cool.