Cut the cucumbers lengthwise into eighths, then cut them crosswise into 2-inch-long sticks. In a large bowl, combine the sesame oil, vinegar and a large pinch of salt. Add the cucumbers and toss well. Let stand for 10 minutes, tossing a few times.
In a mini food processor, combine the sesame seeds, crushed red pepper and 1 1/2 teaspoons of salt. Process until the sesame seeds are coarsely chopped. Add half of the mixture to the cucumbers and toss well. Arrange the cucumbers on a platter. Sprinkle with the remaining sesame seed mixture and the scallions and serve.