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If the sesame seeds you bought are already toasted, you can skip this step. Otherwise, toast the sesame seeds in a dry skillet over low heat, stirring constantly. After about 2 minutes, they will turn golden and fragrant. Pour them onto a small dish so that they can cool off. You can peel them completely, or peel them in alternating stripes for a nicer presentation. Slice the cucumbers in half lengthwise. Scrape the seeds out with a spoon and discard them. You should do this even if you are using a "seedless" variety. You can do this with a sharp knife or a food processor. The slices need to be almost paper thin. Cover your work surface with a paper towel. Spread the cucumbers in an even layer on top, then lay another paper towel on top. Gently pat the paper towel to soak up any excess moisture. Pour the vinegar into a medium-sized serving bowl. Add the sugar and the salt. Stir everything together with a fork or mini whisk until the salt and sugar dissolve. Toss everything together with a pair of salad tongs. Make sure that you grab the cucumbers from the bottom of the bowl as well. Japanese cucumber salad is a great accompaniment to many Japanese dishes, including sushi and sashimi.
Toast the sesame seeds, if needed. Peel the cucumbers. Core the cucumbers. Cut the cucumbers into very thin slices. Press the cucumbers between paper towels to soak up any moisture. Prepare the dressing in the serving bowl. Add the cucumbers the sesame seeds into the bowl. Serve the salad immediately.