Use a vegetable peeler to peel stripes in the cucumbers leaving half the skin. Halve the cucumbers lengthwise. Use spoon to remove the seeds from the cucumber halves. Slice the halves thinly.
Place the cucumber, onion, and 2 teaspoons salt in a bowl with enough water to cover; allow to marinate in refrigerator at least 30 minutes. Drain thoroughly in a colander and transfer to a large bowl; add the jalapeno pepper and carrot to the mixture.
Stir the rice vinegar, ginger, sugar, and pepper together in a small bowl until the sugar is completely dissolved; pour over the cucumber mixture and stir to evenly coat. Cover with plastic wrap and chill in refrigerator at least 30 minutes.
