Using a vegetable peeler, peel carrot, then slice finely lengthways into ribbons.
Cut carrot ribbons into thin strips and place in a bowl with half the salt, then mix well. Place onion slices in a separate bowl with remaining salt and mix well.
Set carrot and onion aside for 1 hour.
Combine vinegar and sugar in a small heavy-based saucepan and stir over medium heat until sugar dissolves. Simmer, uncovered and without stirring, for about 10 minutes, or until reduced and slightly syrupy. Set aside to cool.
Drain carrot and onion and, using your hands, gently squeeze out any excess liquid. Place carrot and onion in the cooled syrup to pickle them lightly.
Using a vegetable peeler, finely slice cucumber lengthways into ribbons and then cut these into thin strips. In a large bowl, combine cucumber with pickled carrot, onion and all remaining ingredients, using your hands to mix thoroughly.
To make the dressing, combine all ingredients in a small bowl. Spoon dressing over salad and serve on a platter.